Showing papers in "Annals of Pure and Applied Logic in 2003"

TL;DR: This work semantically introduces a logic of computability and sets a program for studying various aspects of that logic, and provides illustrations of potential applications of the universal logic in knowledgebase, resourcebase and planning systems, as well as constructive applied theories.

TL;DR: It is shown however that some natural complete Heyting algebra cannot be inductively defined, although many formal topologies can be presented in a predicative way by an inductive generation and thus their properties can be proved inductively.

TL;DR: A new compact formalization of inductive-recursion definitions is given by modeling them as initial algebras in slice categories and it is proved that the elimination and equality rules are equivalent to the principle of the existence of initial alagbras for certain endofunctors.

TL;DR: It is proved that assuming only that T is low, the existentially universal models of the universal part of a natural expansion T P + of T P, are lovely pairs, and “simple Robinson universal domains”.

TL;DR: This paper is the first published one in which a proof-theoretic analysis a la Gentzen–Takeuti of recursively large ordinals is expounded.

TL;DR: An axiomatic development of the theory of apartness and nearness of a point and a set is introduced as a framework for constructive topology.

TL;DR: The quantified hybrid logic of any class of frames definable in the bounded fragment of first-order logic has the interpolation property, irrespective of whether varying, constant, expanding, or contracting domains are assumed.

TL;DR: It is proved that the orbit equivalence relations arising from the natural actions of SL 3 ( Z ) on the projective planes over the various p-adic fields are pairwise incomparable with respect to Borel reducibility.

TL;DR: Describing Δ20-categoricity in Boolean algebras and linear orderings under some extra effectiveness conditions and a study of the relativized notion in these structures is begun.

TL;DR: A characterization of linearity for SU-rank 1 structures is obtained by giving several equivalent conditions on T∗, a “weak” version of local modularity which is equivalent to linearity is found, and it is shown that linearity coincides with 1-basedness.

TL;DR: The result of the analysis of Cheney's proof provides the first effective (in all parameters) uniform modulus of uniqueness (a concept which generalizes ‘strong uniqueness’ studied extensively in approximation theory).

TL;DR: A system of typed terms which corresponds with the classical natural deduction with one conclusion and full logical symbols is defined and Church–Rosser property of the system is proved using an extended method of parallel reduction.

TL;DR: It is proved that no pseudo-elementary class with the independence property is controlled, and by contrast, there is a pseudo-class with the strict order property that is controlled.

TL;DR: It is proved that the determinacy of all Lipschitz games, the determinACY of all Wadge games, and the semi-linear ordering principle for LipsChitz maps are all equivalent.

TL;DR: It is proved that V 1 -Horn, a second-order system of bounded arithmetic formalizing polynomial-time reasoning, is equivalent to QPV and Zambella's P -def, and that the class of ∀ Σ 1 b consequences of S 2 1 is finitely axiomatizable, thus answering an open question.

TL;DR: In this article, the epsilon substitution method is used to prove termination of the H-process for the theory ID1(Π10√Σ10) of non-iterated inductive definitions of simply universal and existential operators.

TL;DR: An extension of natural deduction that is suitable for dealing with modal operators and induction is introduced and a strong normalization theorem for an intuitionistic calculus is proved.

TL;DR: The final results are that CZF extended by Mahlo principles is realizable in corresponding extensions of T 0 , thus providing relative lower bounds for the proof-theoretic strength of the latter.

TL;DR: For every infinite cardinal κ, it is proved that the algebra of transition trees with branching degree is reducible to process algebras with a generalised operation ∑ for choice.

TL;DR: This work studies coset-minimality, as well as two weak versions of the notion: eventual and ultimate cosett-minimal, as a pure ordered group and an eventually cosets of definable subgroups of finite regular rank.

TL;DR: This work defines a cut-elimination procedure which associates with every proof-net of multiplicative and additive linear logic a unique cut-free one in the new notion of additive “multibox” for linear logic proof-nets.

TL;DR: This paper blends techniques of recursion theory with those of topology to establish new findings in recursive analysis and presents several new techniques different from existing ones which yield interesting results.

TL;DR: This paper gives an example of a generic structure whose (full) first-order theory is simple and introduces the notion of semigenericity and shows that if a 〈 K 0 ,≺〉-semigeneric structure exists then EX ( T + ) is an elementary class and therefore the L -theory of 〈詽,⩽-generic is near model complete.

TL;DR: Non- ω -saturated generic structures of the ab initio Hrushovski construction with amalgamation over closed sets are shown to be CM-trivial with weak elimination of imaginaries.

TL;DR: This paper gives a structural characterisation of classes of coalgebras definable by observable formulas, an analogue for polynomial coalge bras of Birkhoff's celebrated characterisations of equationally definable classes of abstract algebr as being those closed under homomorphic images, subalgebra and direct products.

TL;DR: It is shown that T21 and S22 can prove the well-foundedness on bounded domains of the ordinal notations below e0 and Γ0 and, as a corollary, the class of polynomial local search problems, PLS, can be augmented with cost functions that take ordinal values below e 0 andΓ0 without increasing the class PLS.

TL;DR: Let G be a simple group of finite Morley rank with a definable BN-pair of (Tits) rank 2 and G is interpretably isomorphic to PSL3, PSp4(K) or G2 (K) for some algebraically closed field K.

TL;DR: Equiconsistency results concerning gaps between a singular strong limit cardinal κ of cofinality ℵ0 and its power under assumptions that 2κ=κ+δ+1 for δ<κ and some weak form of the Singular Cardinal Hypothesis below κ are proved.

TL;DR: For each infinite cardinal θ⩽κ, the smallest κ-normal ideal J on Pκ(λ) such that J + → κ (J +, θ) 2.

TL;DR: Universes over Frege structures represent a syntactically expressive framework of metapredicative theories in the context of applicative theories and the lower bound is obtained by a syntactic interpretation of these theories.