Showing papers in "Annals of Pure and Applied Logic in 2007"

TL;DR: The reverse directions of the large cardinal axioms of the title are proved and V is definable using the parameter V δ + 1, where δ = P = + .

TL;DR: It is shown that G V is axiomatizable iff V is finite, V is uncountable with 0 isolated in V, or every neighborhood of 0 in V isuncountable.

TL;DR: The simplicity of the quasi-equational form allows an easy predicative constructive proof of the free partial model theorem for cartesian theories: that if a theory morphism is given from one cartesian theory to another, then the forgetful (reduct) functor from one model category to the other has a left adjoint.

TL;DR: It is proved that a variety of Heyting algebras is nuclear iff it is a subframe variety, and that it is dense nuclear ifit is a cofinal sub frame variety.

TL;DR: The Logic of Proofs shows that the deducibility problem is Π 2 p -complete, which is similar to the analogous problem for traditional modal logics is PSPACE-complete.

TL;DR: It is shown how many of these fragments are really distinct and they find axiomatic systems for most of them, and the problem how to axiomatize predicate versions of logics without the lattice disjunction is solved.

TL;DR: A soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic is presented.

TL;DR: In this paper, the authors derive existence results for M-types in locally cartesian closed pretoposes with a natural numbers object, using their internal logic, and use them to prove stability of such categories under various topos-theoretic constructions; namely, slicing, formation of coalgebras (for a cartesian comonad), and sheaves for an internal site.

TL;DR: This work characterize þ-independence in a variety of structures, focusing on the field of real numbers expanded by predicate defining a dense multiplicative subgroup, G, satisfying the Mann property and whose powers are of finite index in G.

TL;DR: This paper gives several characterizations of when the class of modules A with Ext i ( A, N ) = 0 (for fixed N and all i ) is abstract elementary class with respect to the notion that M 1 is a strong submodel M 2 if the quotient remains in the given class.

TL;DR: It is proved that, if V is an effectively given commutative valuation domain such that its value group is dense and archimedean, then the theory of all V -modules is decidable.

TL;DR: It is shown that the results do not apply to the system of classical logic and the results obtain an exponential speed-up between classical and intuitionistic logic.

TL;DR: The Robinson joint consistency theorem for the infinite-valued propositional logic of Łukasiewicz is established: all pre-existing proofs of this latter result make essential use of the Pierce amalgamation theorem for abelian lattice-ordered groups together with the categorical equivalence Γ between these groups and MV-algebras.

TL;DR: This article studies applications of the bounded functional interpretation to theories of feasible arithmetic and analysis to show that the novel, The Hunger Games, is based on this interpretation.

TL;DR: It is shown that there exists a real α such that, for all reals β, if α is linear reducible to β (α≤lβ, previously denoted as α≤swβ) then β≤Tα, and every random real satisfies this quasi-maximality property.

TL;DR: The first goal is to show that the incompleteness results of the prior paper can generalize in this alternate context, and to develop a formal analysis, using a new technique called Passive Induction, that is simpler than the formalism used before.

TL;DR: This work studies OST and some of its most important extensions primarily from a proof-theoretic perspective, determines their consistency strengths by exhibiting equivalent systems in the realm of traditional set theory and introduces a new and interesting extension of OST which is conservative over ZFC.

TL;DR: The linear version of the typed Bohm theorem is studied on a fragment of Intuitionistic Linear Logic and it is shown that in the multiplicative fragment of intuitionistic linear logic without themultiplicative unit 1 (for short IMLL) the weak typed bohm theorem holds.

TL;DR: The exact correspondence between ordinal notations derived from Skolem hull operators and descriptions of ordinals in terms of Σ 1 -elementarity, an approach developed by T.J. Carlson, is analyzed in full detail.

TL;DR: The ind- and pro- categories of the category of definable sets, in some first order theory, are described in terms of points in a sufficiently saturated model.

TL;DR: A toolkit of ordinal arithmetic that generally applies whenever ordinal structures are analyzed whose combinatorial complexity does not exceed the strength of the system KP l 0 of set theory is developed.

TL;DR: A criterion for binarity of ℵ 0 -categorical weakly o-minimal theories in terms of convexity rank is presented.

TL;DR: This paper presents a categorical model for Multiplicative Additive Polarized Linear Logic MALLP, and introduces a notion of polarized ↑ -softness which is a variation of Joyal’s softness to reduce the problem of polarized multiplicative full completeness to the nonpolarized MLL case.

TL;DR: The method of iterated ultrapower representation is developed to provide a unified and perspicuous approach for building automorphisms of countable recursively saturated models of Peano arithmetic PA, and is used to prove Theorem A below, which confirms a long-standing conjecture of James Schmerl.

TL;DR: Sufficient conditions for first-order-based sequent calculi to admit cut elimination by a Schutte–Tait style cut elimination proof are established and the worst case complexity of the cut elimination is analysed.

TL;DR: A constructive (intuitionistic and predicative) proof that the class Hom Loc is a set whenever L is locally compact and L ′ is set-presented and regular is obtained; together with the described compactification, this makes it possible to characterize the class of locales for which Stone–Cech compactification can be defined constructively.

TL;DR: It is shown that if a term inhabits a positive type, then this term is β -normalisable and reduces to a closed term, and positive types can be used to represent abstract data types.

TL;DR: In this paper, it was shown that any definable set in R n can be stratified into cells, whose defining functions are C m smooth Lipschitz continuous functions with constant 2 n 3 / 2, which have additional regularity conditions on the derivatives of higher order derivatives.

TL;DR: A collection of additional sorts in which this theory of A C F p of pairs F K of algebraically closed fields of a given characteristic p has geometric elimination of imaginaries is exhibited.