Showing papers in "Annals of Pure and Applied Logic in 2002"

TL;DR: This paper shows how to transfer a number of computability-theoretic properties from directed graphs to structures in the following classes: symmetric, irreflexive graphs; partial orderings; lattices; rings; rings (with zero-divisors); integral domains of arbitrary characteristic; commutative semigroups; and 2-step nilpotent groups.

TL;DR: A predicative version of topos (stratified pseudotopos) based on the notion of small maps in algebraic set theory, developed by Joyal and one of the authors is introduced.

TL;DR: The paper presents a re"ned method of extracting reasonable and sometimes unexpected programs from classical proofs of formulas of the form ∀x∃yB, since B no longer needs to be quanti"er-free, but only has to belong to a strictly larger class of so-called “goal formulas”.

TL;DR: This chapter shows that SF can also be extended in a very different direction to yield another class SR of ‘computable’ functionals which is in some sense incompatible with PC.

TL;DR: This paper shows that the monodic (not monadic, where this result does not hold) fragment is an exception by constructing its finite Hilbert-style axiomatization.

TL;DR: Categorical proof theory is an approach to understanding the structure of proofs by analyzing G0del's Dialectica interpretation and the Diller-Nahm variant in categorical terms and formulate a proposal as to how to give a more faithful analysis of proofs in the sequent calculus.

TL;DR: This work searched for and found a new property that resembles confluence and that is equivalent to uniqueness of infinite normal forms: skew confluence, and defines the infinite normal form of a term and shows that the infinitenormal form defines a congruence on the set of terms.

TL;DR: The construction of Mitchell and Steel is extended to produce iterable fine structure models which may contain Woodin limits of Woodin cardinals, and more.

TL;DR: The methodology introduced here lends itself to systematic links between natural sub-formalisms and computational complexity classes, and is particularly attractive for the development of Feasible Mathematics.

TL;DR: It is shown that admissible consequence for Σ10-substitutions over HA coincides with NNIL -preservativity over intuitionistic propositional logic ( IPC ), which is the class of propositional formulas with no nestings of implications to the left.

TL;DR: This paper shows that in the presence of (E) , UWKL is much stronger than WKL: whereas WKKL remains to be Π 2 0 -conservative over PRA, PRA ω +(E)+ UWKK contains (and is conservative over) full Peano arithmetic PA.

TL;DR: An axiomatic framework for the non-modular simple ℵ 0 -categorical structures constructed by Hrushovski is given, which allows some of their properties to be verified in a uniform way and to show that these properties are preserved by iterations of the construction.

TL;DR: It is proved the existence of the core model K in the theory “ ZFC +0 •| does not exist”, which provides the last step for determining the exact consistency strength of the assumption in the statement of the 12th Delfino problem.

TL;DR: A semantics for the language of classical first order logic supplemented with the additional operators ⊓ and ⨅ that understands formulas as tasks and can claim to be a formalization of the resource philosophy associated with linear logic, if resources are understood as agents carrying out tasks.

TL;DR: A notion called Herbrand saturation is shown to provide the model-theoretic analogue of a proof- theoretic method, Herbrand analysis, yielding uniform model-Theoretic proofs of a number of important conservation theorems.

TL;DR: Methods for blowing power of singular cardinals using short extenders using long extenders for cardinal preserving extension having the same bounded subsets of κ and satisfying 2 κ =κ +δ+1 for any δ 1 .

TL;DR: A novel approach to constructing natural recursion-theoretic models for (fairly strong) systems of explicit mathematics which is based on nonmonotone inductive definitions is presented.

TL;DR: This work characterize the models of arithmetic in which WPHP fails as those which are determined by an initial segment and proves a conditional separation result in bounded arithmetic, that PV + lies strictly between PV and S21 in strength, assuming that the cryptosystem RSA is secure.

TL;DR: The main result presented here is that the proof theoretic ordinal of CZF − + INAC is a small ordinal known as the Feferman–Schutte ordinal Γ 0 .

TL;DR: The paper explains abstractly the existence of the geometric morphisms and logical functors connecting the various toposes at issue by advancing the theory of triposes over internal partial combinatory algebras and by employing a novel notion of elementary map.

TL;DR: It is shown that for any countable model M of RCA0, there exists a count- able model Mof WKL0 whose first order part is the same as that of M, and whose second order part consists of the M -recursive sets and sets not in the second order parts of M.

TL;DR: There are second-order generalized quantifiers which do not increase expressive power of first-order logic but do increase the power significantly when added to stronger logics, especially with respect to the types of the quantifiers.

TL;DR: In this article, the authors strengthen nonstructure theorems for almost free Abelian groups by studying long Ehrenfeucht-Fraisse games between a fixed group of cardinality λ and a free Abelians group.

TL;DR: This simplification of the characterization of the categories with finite limits whose exact completions are toposes given in Menni allows for new examples and non-examples and to provide a new perspective and an alternative proof on the inevitability of untypedness for realizability toposes.

TL;DR: It is obtained that the free group F 2 (p,ω) in the variety of 2 -nilpotent groups of exponent p>2 with ω free generators has a CM -trivial ω -stable theory.

TL;DR: In this paper, it was shown that in the quotient ring K((G ⩽0 ))/J, each element (not in K ) admits at least one factorization into irreducible.

TL;DR: It is shown that for every computably enumerable (c.e.) degree a > 0 there is an intrinsically c.e. relation on the domain of a computable structure of computable dimension n+1 whose degree spectrum is { a 0,…, a n } .

TL;DR: The thesis is that while the functionals take care of the proof theoretic strength of the interpreted system, it is the functional translation that has to cope with the logical complexities of the system.

TL;DR: This work introduces the notions of Church domain and domain of continuity in order to demonstrate the optimality of “almost negativity” in ECT 0 and GC 1 and shows that intuitionistic analysis with GC 1, MP and DNS 1 is consistent and satisfies Troelstra's and Church's Rules.

TL;DR: The main results are that if U is of cardinality λ+=2λ for some infinite regular cardinal λ, then the set of subgroups of Γ consisting of all pointwise stabilizers of Dcl's of finite subsets of U is invariant under Aut(Γ) (Theorem 2.10).