@article{Baro2012a,
abstract = {In this note, we prove that every definably connected, definably compact abelian definable group G in an o-minimal expansion of a real closed field with dim(G) = 4 is definably homeomorphic to a torus of the same dimension. Moreover, in the semialgebraic case the result holds for all dimensions.},
annote = {First published online 2011},
archiveprefix = {arXiv},
arxivid = {1102.2494},
author = {Baro, El\'{\i}as and Berarducci, Alessandro},
doi = {10.1112/blms/bdr108},
eprint = {1102.2494},
file = {:Users/berardu/Documents/Mendeley Desktop/Baro, Berarducci/Bulletin of the London Mathematical Society/Baro, Berarducci - 2012 - Topology of definable abelian groups in o-minimal structures.pdf:pdf},
issn = {0024-6093},
journal = {Bulletin of the London Mathematical Society},
month = nov,
number = {3},
pages = {473--479},
title = {{Topology of definable abelian groups in o-minimal structures}},
url = {http://blms.oxfordjournals.org/cgi/doi/10.1112/blms/bdr108},
volume = {44},
year = {2012}
}
@article{Berarducci2012a,
abstract = {We work in the category of locally definable groups in an o-minimal expansion of a field. Eleftheriou and Peterzil conjectured that every definably generated abelian connected group G in this category is a cover of a definable group. We prove that this is the case under a natural convexity assumption inspired by the same authors, which in fact gives a necessary and sufficient condition. The proof is based on the study of the zero-dimensional compatible subgroups of G. Given a locally definable connected group G (not necessarily definably generated), we prove that the n-torsion subgroup of G is finite and that every zero-dimensional compatible subgroup of G has finite rank. Under a convexity hypothesis we show that every zero-dimensional compatible subgroup of G is finitely generated.},
archiveprefix = {arXiv},
arxivid = {http://arxiv.org/abs/1202.5649},
author = {Berarducci, Alessandro and Edmundo, M\'{a}rio J. and Mamino, M},
eprint = {/arxiv.org/abs/1202.5649},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Edmundo, Mamino/To appear in Selecta Mathematica/Berarducci, Edmundo, Mamino - 2012 - Discrete subgroups of locally definable groups.pdf:pdf},
journal = {To appear in: Selecta Mathematica},
keywords = {2009wy32e8 003,and phrases,covers,discrete subgroups,locally definable groups,o-minimalit,partially supported by prin},
pages = {1--17},
primaryclass = {http:},
title = {{Discrete subgroups of locally definable groups}},
url = {http://arxiv.org/abs/1202.5649},
year = {2012}
}
@article{Berarducci2012,
abstract = {We study the thresholds for the emergence of various properties in random subgraphs of (N,<). In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the probability is made. The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.},
author = {Berarducci, Alessandro and Majer, Pietro and Novaga, Matteo},
doi = {10.4064/fm216-2-6},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Majer, Novaga/Fundamenta Mathematicae/Berarducci, Majer, Novaga - 2012 - Infinite paths and cliques in random graphs(2).pdf:pdf},
issn = {0016-2736},
journal = {Fundamenta Mathematicae},
number = {2},
pages = {163--191},
title = {{Infinite paths and cliques in random graphs}},
url = {http://journals.impan.pl/cgi-bin/doi?fm216-2-6},
volume = {216},
year = {2012}
}
@article{Berarducci2011c,
author = {Berarducci, Alessandro and Mamino, Marcello},
doi = {10.1112/jlms/jdq080},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Mamino/Journal of the London Mathematical Society/Berarducci, Mamino - 2011 - On the homotopy type of definable groups in an o-minimal structure.pdf:pdf},
issn = {0024-6107},
journal = {Journal of the London Mathematical Society},
month = feb,
number = {3},
pages = {563--586},
title = {{On the homotopy type of definable groups in an o-minimal structure}},
url = {http://jlms.oxfordjournals.org/cgi/doi/10.1112/jlms/jdq080},
volume = {83},
year = {2011}
}
@incollection{Berarducci2011d,
address = {Pisa},
author = {Berarducci, Alessandro},
booktitle = {Matematica, cultura e societa' 2007-2008},
edition = {CRM Series},
editor = {Gabbani, Ilaria},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci/Matematica, cultura e societa' 2007-2008/Berarducci - 2011 - La verit\`{a} matematica da Kant a G\"{o}del.pdf:pdf},
isbn = {978-88-7642-382-6},
pages = {231--254},
publisher = {Scuola Normale Superiore},
title = {{La verit\`{a} matematica da Kant a G\"{o}del}},
url = {http://www.dm.unipi.it/~berardu/Art/2011Verita/cultura-revised2oct2011.pdf},
year = {2011}
}
@article{Berarducci2010c,
abstract = {We study the model theory of “covers” of groups H definable in an o-minimal structure M. We pose the question of whether any finite central extension G of H is interpretable in M, proving some cases (such as when H is abelian) as well as stating various equivalences. When M is an o-minimal expansion of the reals (so H is a definable Lie group) this is related to Milnor’s conjecture [15], and many cases are known. We also prove a strong relative L$\omega$1,$\omega$ -categoricity theorem for universal covers of definable Lie groups, and point out some notable differences with the case of covers of complex algebraic groups (studied by Zilber and his students).},
author = {Berarducci, Alessandro and Peterzil, Ya'acov and Pillay, Anand},
doi = {10.1142/S1793744210000259},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Peterzil, Pillay/Confluentes Mathematici/Berarducci, Peterzil, Pillay - 2010 - Group covers, o-minimality, and categoricity.pdf:pdf},
issn = {1793-7442},
journal = {Confluentes Mathematici},
keywords = {ams subject classification,categoricity,central extension,o-minimal,primary 03c64,secondary 22e15,universal cover},
number = {04},
pages = {473--496},
title = {{Group covers, o-minimality, and categoricity}},
url = {http://www.worldscinet.com/cm/02/0204/S1793744210000259.html},
volume = {02},
year = {2010}
}
@article{Berarducci2010d,
abstract = {It is known that a definably compact group G is an extension of a compact Lie group L by a divisible torsion-free normal subgroup. We show that the o-minimal higher homotopy groups of G are isomorphic to the corresponding higher homotopy groups of L. As a consequence, we obtain that all abelian definably compact groups of a given dimension are definably homotopy equivalent, and that their universal covers are contractible.},
author = {Berarducci, Alessandro and Mamino, Marcello and Otero, Margarita},
doi = {10.1007/s11856-010-0098-6},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Mamino, Otero/Israel Journal of Mathematics/Berarducci, Mamino, Otero - 2010 - Higher homotopy of groups definable in o-minimal structures.pdf:pdf},
issn = {0021-2172},
journal = {Israel Journal of Mathematics},
month = oct,
number = {1},
pages = {143--161},
title = {{Higher homotopy of groups definable in o-minimal structures}},
url = {http://www.springerlink.com/index/10.1007/s11856-010-0098-6},
volume = {180},
year = {2010}
}
@article{Berarducci2009,
abstract = {By recent work on some conjectures of Pillay, each definably compact group in a saturated o-minimal structure is an extension of a compact Lie group by a torsion free normal divisible subgroup, called its infinitesimal subgroup. We show that the infinitesimal subgroup is cohomologically acyclic. This implies that the functorial correspondence between definably compact groups and Lie groups preserves the cohomology.},
author = {Berarducci, Alessandro},
doi = {10.2178/jsl/1245158089},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci/Journal of Symbolic Logic/Berarducci - 2009 - Cohomology of groups in o-minimal structures acyclicity of the infinitesimal subgroup(3).pdf:pdf},
journal = {Journal of Symbolic Logic},
keywords = {2006-08,and phrases,association for symbolic logic,c 2009,cohomology,dgicyt mtm2005-02865,geometr,geor,groups,o-minimality,partially supported by the,project,ıa real},
number = {3},
pages = {891--900},
title = {{Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup}},
url = {http://projecteuclid.org/euclid.jsl/1245158089},
volume = {74},
year = {2009}
}
@article{Berarducci2009c,
abstract = {The topology of definable sets in an o-minimal expansion of a group is not fully understood due to the lack of a triangulation theorem. Despite the general validity of the cell decomposition theorem, we do not know whether any definably compact set is a definable CW-complex. Moreover the closure of an o-minimal cell can have arbitrarily high Betti numbers. Nevertheless we prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language.},
author = {Berarducci, Alessandro and Fornasiero, Antongiulio},
doi = {10.1142/S0219061309000859},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Fornasiero/Journal of Mathematical Logic/Berarducci, Fornasiero - 2009 - o-MINIMAL COHOMOLOGY FINITENESS AND INVARIANCE RESULTS.pdf:pdf},
issn = {0219-0613},
journal = {Journal of Mathematical Logic},
keywords = {mathematics subject classification 2010,o-minimality,primary 03c64,secondary 55n30,shelf cohomology},
number = {2},
pages = {167--182},
title = {{o-MINIMAL COHOMOLOGY: FINITENESS AND INVARIANCE RESULTS}},
url = {http://www.worldscinet.com/jml/09/0902/S0219061309000859.html},
volume = {9},
year = {2009}
}
@article{Berarducci2009h,
abstract = {A metric space X is straight if for each finite cover of X by closed sets, and for each real valued function f on X, if f is uniformly continuous on each set of the cover, then f is uniformly continuous on the whole of X. A locally connected space is straight iff it is uniformly locally connected (ULC). It is easily seen that ULC spaces are stable under finite products. On the other hand the product of two straight spaces is not necessarily straight. We prove that the product X × Y of two metric spaces is straight if and only if both X and Y are straight and one of the following conditions holds: (a) both X and Y are precompact; (b) both X and Y are locally connected; (c) one of the spaces is both precompact and locally connected. In particular, when X satisfies (c), the product X × Z is straight for every straight space Z . Finally, we characterize when infinite products of metric spaces are ULC and we completely solve the problem of straightness of infinite products of ULC spaces.},
author = {Berarducci, Alessandro and Dikranjan, Dikran and Pelant, Jan},
doi = {10.1016/j.topol.2008.12.024},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Dikranjan, Pelant/Topology and its Applications/Berarducci, Dikranjan, Pelant - 2009 - Products of straight spaces.pdf:pdf},
issn = {01668641},
journal = {Topology and its Applications},
month = apr,
number = {7},
pages = {1422--1437},
publisher = {Elsevier B.V.},
title = {{Products of straight spaces}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0166864108004173},
volume = {156},
year = {2009}
}
@article{Berarducci2007b,
abstract = {By recent work on some conjectures of Pillay, each definably compact group G in a saturated o-minimal expansion of an ordered field has a normal “infinitesimal subgroup” G\^{}00 such that the quotient G/G\^{}00, equipped with the “logic topology”, is a compact (real) Lie group. Our first result is that the functor G → G/G\^{}00 sends exact sequences of definably compact groups into exact sequences of Lie groups. We then study the connections between the Lie group G/G\^{}00 and the o-minimal spectrum Spec(G) of G. We prove that G/G\^{}00 is a topological quotient of Spec(G). We thus obtain a natural homomorphism $\Psi$∗ from the cohomology of G/G\^{}00 to the (Cech-)cohomology of G. We show that if G\^{}00 satisfies a suitable contractibility conjecture then G\^{}00 is acyclic in Cech cohomology and $\Psi$∗ is an isomorphism. Finally we prove the conjecture in some special cases.},
author = {Berarducci, Alessandro},
doi = {10.2178/jsl/1203350779},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci/Journal of Symbolic Logic/Berarducci - 2007 - O-minimal spectra, infinitesimal subgroups and cohomology(2).pdf:pdf},
issn = {0022-4812},
journal = {Journal of Symbolic Logic},
keywords = {and phrases,definable group,lie group,o-minimality,type-definable group},
month = dec,
number = {4},
pages = {1177--1193},
title = {{O-minimal spectra, infinitesimal subgroups and cohomology}},
url = {http://projecteuclid.org/euclid.jsl/1203350779},
volume = {72},
year = {2007}
}
@article{Berarducci2007c,
author = {Berarducci, Alessandro and Edmundo, M\'{a}rio J. and Otero, Margarita},
doi = {10.2178/jsl/1191333858},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Edmundo, Otero/Journal of Symbolic Logic/Berarducci, Edmundo, Otero - 2007 - Corrigendum to “Transfer methods for o-minimal topology”.pdf:pdf},
issn = {0022-4812},
journal = {Journal of Symbolic Logic},
month = sep,
number = {3},
pages = {1079--1080},
title = {{Corrigendum to: “Transfer methods for o-minimal topology”}},
url = {http://projecteuclid.org/euclid.jsl/1191333858},
volume = {72},
year = {2007}
}
@article{Berarducci2006,
abstract = {A metric space X is straight if for each finite cover of X by closed sets, and for each real valued function f on X, if f is uniformly continuous on each set of the cover, then f is uniformly continuous on the whole of X. The straight spaces have been studied in [A. Berarducci, D. Dikranjan, J. Pelant, An additivity theorem for uniformly continuous functions, Topology and its Applications 146–147 (2005) 339–352], which contains characterization of the straight spaces within the class of the locally connected spaces (they are the uniformly locally connected ones) and the class of the totally disconnected spaces (they coincide with the totally disconnected Atsuji spaces). We show that the completion of a straight space is straight and we characterize the dense straight subspaces of a straight space. In order to clarify further the relation between straightness and the level of local connectedness of the space we introduce two more intermediate properties between straightness and uniform local connectedness and we give various examples to distinguish them. One of these properties coincides with straightness for complete spaces and provides in this way a useful characterization of complete straight spaces in terms of the behaviour of the quasi-components of the space.},
author = {Berarducci, Alessandro and Dikranjan, Dikran and Pelant, Jan},
doi = {10.1016/j.topol.2005.04.016},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Dikranjan, Pelant/Topology and its Applications/Berarducci, Dikranjan, Pelant - 2006 - Local connectedness and extension of uniformly continuous functions.pdf:pdf;:Users/berardu/Documents/Mendeley Desktop/Berarducci, Dikranjan, Pelant/Topology and its Applications/Berarducci, Dikranjan, Pelant - 2006 - Local connectedness and extension of uniformly continuous functions(2).pdf:pdf},
issn = {01668641},
journal = {Topology and its Applications},
keywords = {locally connected,straight space,uc space,uniformly continuous,uniformly locally connected},
month = nov,
number = {17},
pages = {3355--3371},
title = {{Local connectedness and extension of uniformly continuous functions}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0166864106000691},
volume = {153},
year = {2006}
}
@incollection{Berarducci2004,
abstract = {We give a presentation of various results on zero-groups in o-minimal structures together with some new observations. In particular we prove that if G is a definably connected definably compact group in an o-minimal expansion of a real closed field, then for any maximal definably connected abelian subgroup T of G, G is the union of the conjugates of T. This can be seen as a generalization of the classical theorem that a compact connected Lie group is the union of the conjugates of any of its maximal tori.},
archiveprefix = {arXiv},
arxivid = {math/0511162},
author = {Berarducci, Alessandro},
booktitle = {Lecture Notes in Logic, 29 Logic Colloquium 2004},
editor = {{EDITORS A. ANDRETTA, K. KEARNES}, D. ZAMBELLA},
eprint = {0511162},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci/Lecture Notes in Logic, 29 Logic Colloquium 2004/Berarducci - 2005 - Zero-groups and maximal tori.pdf:pdf},
isbn = {9780521884242},
issn = {1431-5459},
month = nov,
pages = {33--45},
primaryclass = {math},
title = {{Zero-groups and maximal tori}},
url = {http://www.dm.unipi.it/~berardu/Art/2005Tori/03tori-revised.pdf http://arxiv.org/abs/math/0511162},
year = {2005}
}
@article{Berarducci2005,
abstract = {We prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallest (necessarily normal) type-definable subgroup G 00 of bounded index and G/G 00 equipped with the “logic topology” is a compact Lie group. These results give partial answers to some conjectures of the fourth author.},
author = {Berarducci, Alessandro and Otero, Margarita and Peterzil, Ya'acov and Pillay, Anand},
doi = {10.1016/j.apal.2005.01.002},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci et al/Annals of Pure and Applied Logic/Berarducci et al. - 2005 - A descending chain condition for groups definable in o-minimal structures.pdf:pdf},
issn = {01680072},
journal = {Annals of Pure and Applied Logic},
month = jul,
number = {2-3},
pages = {303--313},
title = {{A descending chain condition for groups definable in o-minimal structures}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0168007205000163},
volume = {134},
year = {2005}
}
@article{Berarducci2005a,
abstract = {We consider metric spaces X with the nice property that any continuous function f:X → R which is uniformly continuous on each set of a finite cover of X by closed sets, is itself uniformly continuous. We characterize the spaces with this property within the ample class of all locally connected metric spaces. It turns out that they coincide with the uniformly locally connected spaces, so they include, for instance, all topological vector spaces. On the other hand, in the class of all totally disconnected spaces, these spaces coincide with the UC spaces.},
author = {Berarducci, Alessandro and Dikranjan, Dikran and Pelant, Jan},
doi = {10.1016/j.topol.2003.05.007},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Dikranjan, Pelant/Topology and its Applications/Berarducci, Dikranjan, Pelant - 2005 - An additivity theorem for uniformly continuous functions.pdf:pdf},
issn = {01668641},
journal = {Topology and its Applications},
keywords = {atsuji space,local connectedness,metric spaces,total disconnectedness,uniform continuity},
month = jan,
pages = {339--352},
title = {{An additivity theorem for uniformly continuous functions}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0166864104001543},
volume = {146-147},
year = {2005}
}
@article{Berarducci2004a,
abstract = {Wilkie (Selecta Math. (N.S.) 5 (1999) 397) proved a “theorem of the complement” which implies that in order to establish the o-minimality of an expansion of R with C ∞ functions it suffices to obtain uniform (in the parameters) bounds on the number of connected components of quantifier free definable sets. He deduced that any expansion of R with a family of Pfaffian functions is o-minimal. We prove an effective version of Wilkie’s theorem of the complement, so in particular given an expansion of the ordered field R with finitely many C\^{}∞ functions, if there are uniform and computable upper bounds on the number of connected components of quantifier free definable sets, then there are uniform and computable bounds for all definable sets. In such a case the theory of the structure is effectively o-minimal: there is a recursively axiomatized subtheory such that each of its models is o-minimal. This implies the effective o-minimality of any expansion of R with Pfaffian functions. We apply our results to the open problem of the decidability of the theory of the real \"{y}eld with the exponential function. We show that the decidability is implied by a positive answer to the following problem (raised by van den Dries (in: Logic: From Foundations to applications, Oxford Science Publ., Oxford University Press, New York, 1996, p. 137)): given a language L expanding the language of ordered rings, if an L-sentence is true in every L-structure expanding the ordered field of real numbers, then it is true in every o-minimal L-structure expanding any real closed field.},
author = {Berarducci, Alessandro and Servi, Tamara},
doi = {10.1016/j.apal.2003.08.001},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Servi/Annals of Pure and Applied Logic/Berarducci, Servi - 2004 - An effective version of Wilkie's theorem of the complement and some effective o-minimality results.pdf:pdf},
issn = {01680072},
journal = {Annals of Pure and Applied Logic},
keywords = {o-minimality,pfa an functions,real exponentiation},
month = feb,
number = {1-3},
pages = {43--74},
title = {{An effective version of Wilkie's theorem of the complement and some effective o-minimality results}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0168007203000836},
volume = {125},
year = {2004}
}
@article{Berarducci2004b,
abstract = {Given an o-minimal structure M which expands a field, we define, for each positive integer d, a real-valued additive measure on a Boolean algebra of subsets of M\^{}d and we prove that all the definable sets included in the finite part Fin(M\^{}d) of M\^{}d are measurable. When the domain of M is the real line we obtain Lebesgue measure, but restricted to a proper subalgebra of that of the Lebesgue measurable sets (the Jordan measurable sets). Our measure has good logical properties, being invariant under elementary extensions and under expansions of the language. In the final part of the paper we consider the problem of defining an analogue of the Haar measure for definably compact groups.},
author = {Berarducci, Alessandro and Otero, Margarita},
doi = {10.1093/qmath/hah010},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Otero/The Quarterly Journal of Mathematics/Berarducci, Otero - 2004 - An additive measure in o-minimal expansions of fields.pdf:pdf},
issn = {0033-5606},
journal = {The Quarterly Journal of Mathematics},
month = dec,
number = {4},
pages = {411--419},
title = {{An additive measure in o-minimal expansions of fields}},
url = {http://qjmath.oxfordjournals.org/cgi/doi/10.1093/qmath/hah010},
volume = {55},
year = {2004}
}
@article{Berarducci2003,
abstract = {Let M be an o-minimal expansion of an ordered field. Let $\phi$ be a formula in the language of ordered domains. In this note we establish some topological properties which are transferred from $\phi$M to $\phi$ℝ and vice versa. Then, we apply these transfer results to give a new proof of a result of M. Edmundo—based on the work of A. Strzebonski—showing the existence of torsion points in any definably compact group defined in an o-minimal expansion of an ordered field.},
author = {Berarducci, Alessandro and Otero, Margarita},
doi = {10.2178/jsl/1058448438},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Otero/Journal of Symbolic Logic/Berarducci, Otero - 2003 - Transfer methods for o-minimal topology.pdf:pdf},
issn = {0022-4812},
journal = {Journal of Symbolic Logic},
month = sep,
number = {3},
pages = {785--794},
publisher = {Association for Symbolic Logic},
title = {{Transfer methods for o-minimal topology}},
url = {http://projecteuclid.org/euclid.jsl/1058448438},
volume = {68},
year = {2003}
}
@article{Berarducci2002c,
abstract = {The definable fundamental group of a definable set in an o-minimal expansion of a field is computed. This is achieved by proving the relevant case of the o-minimal van Kampen theorem. This result is applied to show that if the geometrical realization of a simplicial complex over an o-minimal expansion of a field is a definable manifold of dimension not 4, then its geometrical realization over the reals is a topological manifold.},
author = {Berarducci, Alessandro and Otero, Margarita},
doi = {10.1112/S0024610701003015},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Otero/Journal of the London Mathematical Society/Berarducci, Otero - 2002 - o-Minimal Fundamental Group, Homology and Manifolds.pdf:pdf},
isbn = {0024610701003},
issn = {0024-6107},
journal = {Journal of the London Mathematical Society},
month = apr,
number = {2},
pages = {257--270},
title = {{o-Minimal Fundamental Group, Homology and Manifolds}},
url = {http://jlms.oxfordjournals.org/cgi/doi/10.1112/S0024610701003015},
volume = {65},
year = {2002}
}
@article{Berarducci2002,
abstract = {We prove that every complete metric space X that is thin (i.e., every closed subspace has connected uniform quasi components) has the compact separation property (for any two disjoint closed connected subspaces A and B of X there is a compact set K disjoint from A and B such that every neighbourhood of K disjoint from A and B separates A and B). The real line and all compact spaces are obviously thin. We show that a space is thin if and only if it does not contain a certain forbidden configuration. Finally we prove that every metric UA-space (see [Rend. Instit. Mat. Univ. Trieste 25 (1993) 23–56]) is thin. The UA-spaces form a class properly including the Atsuji spaces.},
author = {Berarducci, Alessandro and Dikranjan, Dikran and Pelant, Jan},
doi = {10.1016/S0166-8641(01)00132-8},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Dikranjan, Pelant/Topology and its Applications/Berarducci, Dikranjan, Pelant - 2002 - Uniform quasi components, thin spaces and compact separation.pdf:pdf},
issn = {01668641},
journal = {Topology and its Applications},
keywords = {compact,metric spaces,quasi component,real-valued functions,thin spaces},
month = jul,
number = {1-2},
pages = {51--64},
title = {{Uniform quasi components, thin spaces and compact separation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0166864101001328},
volume = {122},
year = {2002}
}
@article{Berarducci2002b,
abstract = {The uniformly approachable functions introduced in [Quaestiones Math. 18 (1995) 381–396] are defined by a property stronger than continuity and weaker than uniform continuity, which is preserved under composition. (So they give rise to a category which sits between the category of metric spaces with all continuous functions and the category of metric spaces with all uniformly continuous functions.) Solving a problem left open in [Rend. Istit. Mat. Univ. Trieste 25 (1993) 23– 56], we give a complete characterization of the polynomial maps f : Rn → R which are uniformly approachable. They coincide with the polynomial maps f with distant fibers, i.e., such that any two distinct fibers f −1 (x) and f −1 (y) are at positive distance. The same holds more generally for any real valued function on Rn whose fibers have finitely many connected components. To prove this we show that every real valued continuous function with distant fibers on a uniformly locally connected metric space is uniformly approachable, and any (weakly) uniformly approachable function on Rn has “distant connected components of fibers”. We observe that a bounded continuous function f : Rn → R has distant fibers if and only if it is uniformly continuous. This suggests that for a reasonable metric space X the uniform continuity of a bounded continuous function f : X → R depends only on the fibers of f . We show that this is the case when X is connected and locally connected. A useful tool in the study of uniformly approachable functions on domains more general than Rn is given by the technique of “truncations” (g is a truncation of f if it is locally constant where it differs from f ). On Rn the functions with many uniformly continuous truncations coincide with the functions with distant connected components of fibers. We improve the technique of the magic set introduced in [Rend. Istit. Mat. Univ. Trieste 25 (1993) 23–56] and studied by M.R. Burke and K. Ciesielski showing that every continuous function with “small fibers” on a locally arcwise connected metric space X has a magic set M ⊂ X (i.e., every continuous g : X → R with g(M) ⊂ f (M) is a truncation of f )},
author = {Berarducci, Alessandro and Dikranjan, Dikran and Pelant, Jan},
doi = {10.1016/S0166-8641(01)00105-5},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Dikranjan, Pelant/Topology and its Applications/Berarducci, Dikranjan, Pelant - 2002 - Functions with distant fibers and uniform continuity.pdf:pdf},
issn = {01668641},
journal = {Topology and its Applications},
keywords = {approachable functions,metric spaces,real valued functions,unicoherence},
month = jun,
number = {1-2},
pages = {3--23},
title = {{Functions with distant fibers and uniform continuity}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0166864101001055},
volume = {121},
year = {2002}
}
@inproceedings{Berarducci2001a,
abstract = {Extensions of the simply typed lambda calculus have been used as a metalanguage to represent “higher order term algebras”, such as, for instance, formulas of the predicate calculus. In this representation bound variables of the object language are represented by bound variables of the metalanguage. This choice has various advantages but makes the notion of “recursive definition” on higher order term algebras more subtle than the corresponding notion on first order term algebras. Despeyroux, Pfenning and Schurmann pointed out the problems that arise in the proof of a canonical form theorem when one combines higher order representations with primitive recursion. In this paper we consider a stronger scheme of recursion and we prove that it captures all partial recursive functions on second order term alge- bras. We illustrate the system by considering typed programs to reduce to normal form terms of the untyped lambda calculus, encoded as ele- ments of a second order term algebra. First order encodings based on de Bruijn indexes are also considered. The examples also show that a version of the intersection type disciplines can be helpful in some cases to prove the existence of a canonical form. Finally we consider interpretations of our typed systems in the pure lambda calculus and a new goedelization the pure lambda calculus.},
author = {Berarducci, Alessandro and B\"{o}hm, Corrado},
booktitle = {Rewriting Techniques and Applications},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, B\"{o}hm/Rewriting Techniques and Applications/Berarducci, B\"{o}hm - 2001 - General recursion on second order term algebras.pdf:pdf},
pages = {15--30},
publisher = {Springer},
title = {{General recursion on second order term algebras}},
url = {http://www.springerlink.com/index/60980E5JG663V58E.pdf},
year = {2001}
}
@article{Berarducci2001,
abstract = {We develop an intersection theory for definable C\^{}p -manifolds in an o-minimal expansion of a real closed field and we prove the invariance of the intersection numbers under definable C\^{}p -homotopies (p > 2). In particular we define the intersection number of two definable submanifolds of complementary dimensions, the Brouwer degree and the winding numbers. We illustrate the theory by deriving in the o-minimal context the Brouwer fixed point theorem, the Jordan-Brouwer separation theorem and the invariance of the Lefschetz numbers under definable C\^{}p -homotopies. A. Pillay has shown that any definable group admits an abstract manifold structure. We apply the intersection theory to definable groups after proving an embedding theorem for abstract definably compact C\^{}p -manifolds. In particular using the Lefschetz fixed point theorem we show that the Lefschetz number of the identity map on a definably compact group, which in the classical case coincides with the Euler characteristic, is zero.},
author = {Berarducci, Alessandro and Otero, Margarita},
doi = {10.1016/S0168-0072(00)00027-0},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Otero/Annals of Pure and Applied Logic/Berarducci, Otero - 2001 - Intersection theory for o-minimal manifolds.pdf:pdf},
issn = {01680072},
journal = {Annals of Pure and Applied Logic},
keywords = {o-minimality},
month = jan,
number = {1-3},
pages = {87--119},
title = {{Intersection theory for o-minimal manifolds}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0168007200000270},
volume = {107},
year = {2001}
}
@incollection{Berarducci1999b,
author = {Berarducci, Alessandro and Intrigila, Benedetto},
booktitle = {Logic and foundations of mathematics},
isbn = {9780792356592},
pages = {67--81},
publisher = {Kluwer Academic Publisher},
title = {{Linear recursive relations are Delta\_0 definable.}},
year = {1999}
}
@article{Berarducci1999a,
abstract = {Recent work on infinitary versions of the lambda calculus has shown that the infinite lambda calculus can be a useful tool to study the unsolvable terms of the classical lambda calculus. Working in the framework of the intersection type disciplines, we devise a type assignment system such that two terms are equal in the infinite lambda calculus iff they can be assigned the same types in any basis. A novel feature of the system is the presence of a type constant to denote the set of all terms of order zero, and the possibility of applying a type to another type. We prove a completeness and an approximation theorem for our system. Our results can be considered as a first step towards the goal of giving a denotational semantics for the lambda calculus which is suited for the study of the unsolvable terms. However, some noncontinuity phenomena of the infinite lambda calculus make a full realization construction of a filter model) a quite difficult task.},
author = {Berarducci, Alessandro and Dezani-Ciancaglini, M},
doi = {10.1016/S0304-3975(98)00135-2},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Dezani-Ciancaglini/Theoretical Computer Science/Berarducci, Dezani-Ciancaglini - 1999 - Infinite $\lambda$-calculus and types.pdf:pdf},
issn = {03043975},
journal = {Theoretical Computer Science},
keywords = {infinite i-calculus},
month = feb,
number = {1-2},
pages = {29--75},
title = {{Infinite $\lambda$-calculus and types}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0304397598001352},
volume = {212},
year = {1999}
}
@article{Berarducci1999,
abstract = {The field of generalized power series with real coefficients and exponents in an ordered abelian divisible group G is a classical tool in the study of real closed fields. We prove the existence of irreducible elements in the ring R((G≤0)) consisting of the generalized power series with non-positive exponents. The following candidate for such an irreducible series was given by Conway (1976): Sum\_n t\^{}(−1/n) + 1. Gonshor (1986) studied the question of the existence of irreducible elements and obtained necessary conditions for a series to be irreducible. We show that Conway’s series is indeed irreducible. Our results are based on a new kind of valuation taking ordinal numbers as values. If G = (R, +, 0, ≤) we can give the following test for irreducibility based only on the order type of the support of the series: if the order type $\alpha$ is either $\omega$ or of the form $\omega$\^{}$\omega$\^{}$\alpha$ and the series is not divisible by any monomial, then it is irreducible. To handle the general case we use a suggestion of M.-H. Mourgues, based on an idea of Gonshor, which allows us to reduce to the special case G = R. In the final part of the paper we study the irreducibility of series with finite support.},
author = {Berarducci, Alessandro},
doi = {10.1090/S0002-9947-99-02172-8},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci/Transactions of the American Mathematical Society/Berarducci - 1999 - Factorization in generalized power series.pdf:pdf},
journal = {Transactions of the American Mathematical Society},
number = {2},
pages = {553--577},
title = {{Factorization in generalized power series}},
url = {http://www.ams.org/journals/tran/2000-352-02/S0002-9947-99-02172-8/},
volume = {352},
year = {1999}
}
@article{Berarducci1998,
abstract = {We study the poset B(G) of all precompact Hausdorff group topologies on an infinite group G and its subposet B(G)w of topologies of weight w, extending earlier results of Berhanu, Comfort, Reid, Remus, Ross, Dikranjan, and others. We show that if B(G)w is non-empty and the power set of G/G' has the same size as the power set of G (in particular, if G is abelian) then the poset of all subsets of 2\^{}G of size w can be embedded into B(G)w (and vice versa). So the study of many features (depth, height, width, size of chains, etc.) of the poset B(G)w is reduced to purely set-theoretical problems. We introduce a cardinal function Ded*(w) to measure the length of chains of subsets of cardinality w of a set of larger cardinality generalizing the well-known cardinal function Ded(w). We prove that Ded*(w) = Ded(w) iff the cofinality of Ded(w) is different from w\^{}+ and we use earlier results of Mitchell and Baumgartncr to show that Ded*(aleph\_1 ) = Ded(aleph\_1) is independent of Zermelc+Fraenkel set theory (ZFC). We apply this result to show that it cannot be established in ZFC whether B(G)aleph\_1 has chains of bigger size than those of the bounded chains. We prove that the poset B(G)aleph\_0 of all Hausdorff metrizable group topologies on the group G = (direct sum of aleph\_0 copies of Z/2Z) has uncountable depth, hence cannot be embedded into B(G)aleph\_0. This is to be contrasted with the fact that for every infinite abelian group G the poset H(G) of all Hausdorff group topologies on G can be embedded into B(G). We also prove that it is independent of ZFC whether the poset H(G)aleph\_0 has the same height as the poset B(G)aleph\_0},
author = {Berarducci, Alessandro and Dikranjan, Dikran and Forti, Marco and Watson, S.},
doi = {10.1016/S0022-4049(96)00149-1},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci et al/Journal of Pure and Applied Algebra/Berarducci et al. - 1998 - Cardinal invariants and independence results in the poset of precompact group topologies.pdf:pdf},
issn = {0022-4049},
journal = {Journal of Pure and Applied Algebra},
number = {1-3},
pages = {19--49},
publisher = {Elsevier},
title = {{Cardinal invariants and independence results in the poset of precompact group topologies}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022404996001491},
volume = {126},
year = {1998}
}
@incollection{Berarducci1996a,
abstract = {We treat a general technique to obtain Church - Rosser extensions of the lambda-beta-calculus, based on the notion of ``confining class'' and on an infinitary version of lambda-calculus. We apply the technique to find a large class of terms which can be consistently equated to every other term, and we also show that many equations between lambda-terms can be consistently added to the the lambda-beta-calculus.},
author = {Berarducci, Alessandro and Intrigila, Benedetto},
booktitle = {Logic: from Foundations to Applicatios},
chapter = {2},
editor = {Hodges, Wilfrid and Hyland, Martin and Steinhorn, Charles and Truss, John},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Intrigila/Logic from Foundations to Applicatios/Berarducci, Intrigila - 1996 - Church-Rosser lambda-theories, Infinite lambda-terms and consistency problems.pdf:pdf},
isbn = {0 19 853862 6},
pages = {33--58},
title = {{Church-Rosser lambda-theories, Infinite lambda-terms and consistency problems}},
url = {http://www.dm.unipi.it/~berardu/Art/1996Church/CRtheories.pdf},
year = {1996}
}
@incollection{Berarducci1996b,
abstract = {We define a model of the lambda-beta-calculus which is similar to the model of Boehm trees, but it does not identify all the unsolvable lambda-terms. The role of the unsolvable terms is taken by a much smaller class of terms which we call mute. Mute terms are those zero terms which are not beta-convertible to a zero term applied to something else. We prove that it is consistent with the lambda-beta-calculus to simultaneously equate all the mute terms to a fixed arbitrary closed term. This allows us to strengthen some results of Jacopini and Venturini Zilli concerning easy lambda-terms. Our results depend on an infinitary version of lambda-calculus. We set the foundations for such a calculus, which might turn out to be a useful tool for the study of non-sensible models of lambda-calculus.},
author = {Berarducci, Alessandro},
booktitle = {LOGIC AND ALGEBRA, Lecture Notes in Pure and Applied Mathematics Series/180},
editor = {Ursini, Aldo and Aglian\`{o}, Paolo},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci/LOGIC AND ALGEBRA, Lecture Notes in Pure and Applied Mathematics Series180/Berarducci - 1996 - Infinite lambda-calculus and non-sensible models.pdf:pdf},
pages = {339--378},
title = {{Infinite lambda-calculus and non-sensible models}},
url = {http://www.dm.unipi.it/~berardu/Art/1996Nonsensible/non-sensible.pdf},
year = {1996}
}
@article{Berarducci1996,
abstract = {Models of normal open induction are those normal discretely ordered rings whose nonnegative part satisfy Peano's axioms for open formulas in the language of ordered semirings. (Where normal means integrally closed in its fraction field.) In 1964 Shepherdson gave a recursive nonstandard model of open induction. His model is not normal and does not have any infinite prime elements. In this paper we present a recursive nonstandard model of normal open induction with an unbounded set of infinite prime elements.},
author = {Berarducci, Alessandro and Otero, Margarita},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Otero/The Journal of Symbolic Logic/Berarducci, Otero - 1996 - A Recursive Nonstandard Model of Normal Open Induction.pdf:pdf},
journal = {The Journal of Symbolic Logic},
number = {4},
pages = {1228--1241},
title = {{A Recursive Nonstandard Model of Normal Open Induction}},
url = {http://www.jstor.org/discover/10.2307/2275813?uid=3738296\&uid=2\&uid=4\&sid=21101465493507 http://projecteuclid.org/euclid.jsl/1183745132},
volume = {61},
year = {1996}
}
@article{D'Aquino1995,
abstract = {We prove that if G is a Delta\_0 definable function on the natural numbers and F(n) is the product of the first n values of G, then F is also Delta\_0 definable. Moreover, the inductive properties of F can be proved inside the theory IDelta\_0.},
author = {Berarducci, Alessandro and D'Aquino, Paola},
doi = {10.1016/0168-0072(94)00055-8},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, D'Aquino/Annals of Pure and Applied Logic/Berarducci, D'Aquino - 1995 - $\Delta$0-complexity of the relation y = $\Pi$i ⩽ nF(i).pdf:pdf},
issn = {01680072},
journal = {Annals of Pure and Applied Logic},
month = sep,
number = {1-2},
pages = {49--56},
title = {{$\Delta$0-complexity of the relation y = $\Pi$i ⩽ nF(i)}},
url = {http://www.sciencedirect.com/science/article/pii/0168007294000558 http://linkinghub.elsevier.com/retrieve/pii/0168007294000558},
volume = {75},
year = {1995}
}
@article{Berarducci1993c,
abstract = {The cop number c(G) of a graph G is an invariant connected with the genus and the girth. We prove that for a fixed k there is a polynomial-time algorithm which decides whether c(G) ≤ k. This settles a question of T. Andreae. Moreover, we show that every graph is topologically equivalent to a graph with c ≤ 2. Finally we consider a pursuit-evasion problem in Littlewood′s miscellany. We prove that two lions are not always sufficient to catch a man on a plane graph, provided the lions and the man have equal maximum speed. We deal both with a discrete motion (from vertex to vertex) and with a continuous motion. The discrete case is solved by showing that there are plane graphs of cop number 3 such that all the edges can be represented by straight segments of the same length.},
author = {Berarducci, Alessandro and Intrigila, Benedetto},
doi = {10.1006/aama.1993.1019},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Intrigila/Advances in Applied Mathematics/Berarducci, Intrigila - 1993 - On the cop number of a graph.pdf:pdf},
journal = {Advances in Applied Mathematics},
pages = {389--403},
title = {{On the cop number of a graph}},
url = {http://www.sciencedirect.com/science/article/pii/S0196885883710195},
volume = {14},
year = {1993}
}
@article{Berarducci1993,
abstract = {Uniformly approachable (UA) functions are a common generalization of uniformly continuous functions an d perfect functions. We study UA-functions and UA-spaces i. e. those uniform spaces in which every real valued continuous function is UA. Such spaces properly include the UC-spaces (Atsuji spaces). We characterize the weakly-UA subspaces of the real line and give a new characterization of the UC spaces. We prove a topological result which implies, under the continuum hypothesis, the existence of a subset M of the the n-dimensional euclidean space R\^{}n such that if two continuous functions f, g from R\^{}n to R are are not constant on any open set and g(M) is a subset of f(M), then f=g.},
author = {Berarducci, Alessandro and Dikranjan, Dikran},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Dikranjan/Rendiconti dell’Istituto di Matematica dell’Universit\`{a} di Trieste. An International Journal of Mathematics/Berarducci, Dikranjan - 1993 - Uniformly approachable functions and spaces.pdf:pdf},
journal = {Rendiconti dell’Istituto di Matematica dell’Universit\`{a} di Trieste. An International Journal of Mathematics},
pages = {23--53},
title = {{Uniformly approachable functions and spaces}},
url = {http://hdl.handle.net/10077/4683},
volume = {25},
year = {1993}
}
@article{Berarducci1993e,
abstract = {Given two closed lambda-terms A and B we consider the question whether the equation A = B is consistent with the lambda-beta-calculus. In general the problem is undecidable. However if A is a 0-term we can give good sufficient conditions for the consistency. This allows us to prove some counterintuitive results such as: (1) there is a closed lambda-term X which can be consistently equated to every closed lambda-term with the exception of the identity lambda x.x. (2) there is a closed lambda-term which can be consistenlty equated to every closed normal form, but not to the Curry fixed point operator Y.},
author = {Berarducci, Alessandro and Intrigila, Benedetto},
doi = {10.1016/0304-3975(93)90084-7},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Intrigila/Theoretical Computer Science/Berarducci, Intrigila - 1993 - Some new results on easy lambda-terms.pdf:pdf},
issn = {03043975},
journal = {Theoretical Computer Science},
keywords = {lambda-calculus},
month = dec,
number = {1-2},
pages = {71--88},
publisher = {Elsevier},
title = {{Some new results on easy lambda-terms}},
url = {http://www.sciencedirect.com/science/article/pii/0304397593900847 http://linkinghub.elsevier.com/retrieve/pii/0304397593900847},
volume = {121},
year = {1993}
}
@article{Berarducci1993b,
abstract = {Let PL$\omega$ be the provability logic of I$\Delta$0 + $\omega$1. We prove some containments of the form L ⊆ PL$\omega$ < Th(C) where L is the provability logic of PA and Th(C) is a suitable class of Kripke frames.},
author = {Berarducci, Alessandro and Verbrugge, Rineke},
doi = {10.1016/0168-0072(93)90199-N},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Verbrugge/Annals of Pure and Applied Logic/Berarducci, Verbrugge - 1993 - On the provability logic of bounded arithmetic.pdf:pdf},
issn = {01680072},
journal = {Annals of Pure and Applied Logic},
month = may,
number = {1-2},
pages = {75--93},
title = {{On the provability logic of bounded arithmetic}},
url = {http://linkinghub.elsevier.com/retrieve/pii/016800729390199N},
volume = {61},
year = {1993}
}
@article{Berarducci1993a,
abstract = {We define a general notion of (syntactic) unification, whose special cases are matching, unification, semi-unification, and weak-unification. We settle all the implications between the various cases of unification leading to a classification and a decidability result. We show that some distinctions holding for finite terms collapse for infinite terms. We give some positive results on the existence of most general weak-unifiers.},
author = {Berarducci, Alessandro and Zilli, Marisa Venturini},
doi = {10.1006/jsco.1993.1059},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Zilli/Journal of Symbolic Computation/Berarducci, Zilli - 1993 - Generalizations of unification.pdf:pdf},
issn = {07477171},
journal = {Journal of Symbolic Computation},
month = nov,
number = {5},
pages = {479--491},
publisher = {Elsevier},
title = {{Generalizations of Unification}},
url = {http://www.sciencedirect.com/science/article/pii/S074771718371059X http://linkinghub.elsevier.com/retrieve/pii/S074771718371059X},
volume = {16},
year = {1993}
}
@incollection{Berarducci1993d,
abstract = {We formalize a technique introduced by B$\backslash$"\{o\}hm and Piperno to solve systems of recursive equations in lambda calculus without the use of the fixed point combinator and using only normal forms. To this aim we introduce the notion of a canonical algebraic term rewriting system, and we show that any such system can be interpreted in the lambda calculus by the B$\backslash$"\{o\}hm - Piperno technique in such a way that strong normalization is preserved. This allows us to improve some recent results of Mogensen concerning efficient g$\backslash$"\{o\}delizations \$\backslash godel\{\~{}\}: \backslash Lambda \backslash rightarrow \backslash Lambda\$ of lambda calculus. In particular we prove that under a suitable g$\backslash$"\{o\}delization there exist two lambda terms \$\backslash bf E\$ (self-interpreter) and \$\backslash bf R\$ (reductor), both having a normal form, such that for every (closed or open) lambda term \$M\backslash;\$ \$\{\backslash bf E\}\backslash godel\{M\} \backslash reduce M\$ and if \$M\$ has a normal form \$N\$, then \$\{\backslash bf R\}\backslash godel\{M\} \backslash reduce \backslash godel\{N\}\$.},
address = {Berlin, Heidelberg},
author = {Berarducci, Alessandro and B\"{o}hm, Corrado},
booktitle = {Computer Science Logic. 6th Workshop, CSL '92 San Miniato, Italy, September 28 – October 2, 1992 Selected Papers. LECTURE NOTES IN COMPUTER SCIENCE, vol. 702},
doi = {10.1007/3-540-56992-8},
editor = {B\"{o}rger, E and J\"{a}ger, G and {Kleine B\"{u}ning}, H and Martini, S and Richter, M. M.},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, B\"{o}hm/Computer Science Logic. 6th Workshop, CSL '92 San Miniato, Italy, September 28 – October 2, 1992 Selected Papers. LECTURE NOTES IN COMPUTER SCIENCE, vol. 702/Berarducci, B\"{o}hm - 1993 - A self interpreter of lambda-calculus having a normal form.pdf:pdf},
isbn = {978-3-540-56992-3},
number = {section 2},
pages = {85--99},
publisher = {Springer Berlin Heidelberg},
series = {Lecture Notes in Computer Science},
title = {{A self interpreter of lambda-calculus having a normal form}},
url = {http://www.springerlink.com/index/7v1168741x4w1274.pdf http://www.springerlink.com/index/10.1007/3-540-56992-8},
volume = {702},
year = {1993}
}
@incollection{Berarducci1991a,
abstract = {It is well known that in bounded arithmetic one can code sequences and recursive definitions using bounded formulas. We present a way of doing this with the help of a notion of pseudo-sequence. Pseudo sequences can be concatenated but do not possess a primitive for extracting the n-th element.},
address = {Siena},
author = {Berarducci, Alessandro and Intrigila, Benedetto},
booktitle = {Technical Report n. 231},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Intrigila/Technical Report n. 231/Berarducci, Intrigila - 1991 - A note on coding techniques in bounded arithmetic.pdf:pdf},
pages = {1--12},
publisher = {Dipartimento di Matematica, Via del Capitano 15, Universi\`{a} di Siena},
title = {{A note on coding techniques in bounded arithmetic}},
url = {http://www.dm.unipi.it/~berardu/Art/1991Coding/coding.pdf},
year = {1991}
}
@article{Berarducci1991,
abstract = {We prove that the theory I$\Delta$0, extended by a weak version of the $\Delta$0-Pigeonhole Principle, proves that every integer is the sum of four squares (Lagrange's theorem). Since the required weak version is derivable from the theory I$\Delta$0 + ∀x (xlog(x) exists), our results give a positive answer to a question of Macintyre (1986). In the rest of the paper we consider the number-theoretical consequences of a new combinatorial principle, the ‘$\Delta$0-Equipartition Principle’ ($\Delta$0EQ). In particular we give a new proof, which can be formalized in I$\Delta$0 + $\Delta$0EQ, of the fact that every prime of the form 4n + 1 is the sum of two squares.},
author = {Berarducci, Alessandro and Intrigila, Benedetto},
doi = {10.1016/0168-0072(91)90096-5},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, Intrigila/Annals of Pure and Applied Logic/Berarducci, Intrigila - 1991 - Combinatorial principles in elementary number theory.pdf:pdf},
issn = {01680072},
journal = {Annals of Pure and Applied Logic},
month = nov,
number = {1},
pages = {35--50},
title = {{Combinatorial principles in elementary number theory}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0168007291900965},
volume = {55},
year = {1991}
}
@article{Berarducci1990,
author = {Berarducci, Alessandro},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci/Journal of Symbolic Logic/Berarducci - 1990 - The Interpretability Logic of Peano Arithmetic.pdf:pdf},
issn = {0022-4812},
journal = {Journal of Symbolic Logic},
number = {3},
pages = {1059--1089},
publisher = {JSTOR},
title = {{The Interpretability Logic of Peano Arithmetic}},
url = {http://www.jstor.org/stable/2274474},
volume = {55},
year = {1990}
}
@article{Berarducci1989,
abstract = {We consider the predicative modal provability logic of Peano Arithmetic where the interpretation of each atomic modal formulas is required to be belong to the set of arithmetic formulas of complexity Sigma\_0\^{}n. We show that for distinct values of n the corresponding modal formulas form a strict hierarchy and each of them is complete for the class Pi\^{}0\_2.},
author = {Berarducci, Alessandro},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci/Bollettino U.M.I/Berarducci - 1989 - Sigma\_0n interpretations of modal logic.pdf:pdf},
journal = {Bollettino U.M.I.},
number = {3-A},
pages = {177--184},
title = {{Sigma\_0\^{}n interpretations of modal logic}},
volume = {7},
year = {1989}
}
@incollection{Berarducci1989a,
author = {Berarducci, Alessandro},
booktitle = {Atti degli incontri di logica matematica, vol. 6},
editor = {{Dipartimento di Matematica, Via del Capitano 15}, Siena},
pages = {75--83},
title = {{MODAL LOGIC AND INTERPRETABILITY}},
year = {1989}
}
@article{Berarducci1985,
abstract = {The notion of iteratively defined functions from and to heterogeneous term algebras is introduced as the solution of a finite set of equations of a special shape. Such a notion has remarkable consequences: (1) Choosing the second-order typed lambda- calculus (Lambsa for short) as a programming language enables one to represent algebra elements and iterative functions by automatic uniform synthesis paradigms, using neither conditional nor recursive constructs. (2) A completeness theorem for Lambda-terms with type of degree at most two and a companion corollary for Lambda-programs have been proved. (3) A new congruence relation for the last-mentioned Lambda-terms which is stronger than Lambda-convertibility is introduced and proved to have the meaning of a Lambda-program equivalence. Moreover, an extension of the paradigms to the synthesis of functions of higher complexity is considered and exemplified. All the concepts are explained and motivated by examples over integers, list- and tree-structures.},
author = {Berarducci, Alessandro and B\"{o}hm, Corrado},
doi = {10.1016/0304-3975(85)90135-5},
file = {:Users/berardu/Documents/Mendeley Desktop/Berarducci, B\"{o}hm/Theoretical Computer Science/Berarducci, B\"{o}hm - 1985 - Automatic synthesis of typed Lambda-programs on term algebras.pdf:pdf},
journal = {Theoretical Computer Science},
number = {820076097},
pages = {135--154},
publisher = {Elsevier},
title = {{Automatic synthesis of typed [Lambda]-programs on term algebras}},
url = {http://www.sciencedirect.com/science/article/pii/0304397585901355},
volume = {39},
year = {1985}
}
@incollection{Berarducci1984,
author = {Berarducci, Alessandro},
booktitle = {Atti degli incontri di logica matematica, vol. 2},
editor = {{Dipartimento di Matematica - Universit\`{a} di Siena}},
pages = {467--476},
title = {{Una generalizzazione dei funzionali ricorsivi di G\"{o}del}},
year = {1984}
}
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