Showing papers in "Annals of Pure and Applied Logic in 2016"

TL;DR: It is proved that several interesting propositional logics of dependence, including propositional dependence logic, propositional intuitionistic dependence logic as well as propositional inquisitive logic, are expressively complete and have disjunctive or conjunctive normal forms.

TL;DR: It is shown that whenever AEC classes are categorical in a high-enough cardinal, they admit a good frame: a forking-like notion for types of singleton elements, and deduce (modulo an unproven claim of Shelah) that Shelah's eventual categoricity conjecture for AECs follows from the weak generalized continuum hypothesis and a large cardinal axiom.

TL;DR: It is proved that in any given AEC, there can exist at most one independence relation that satisfies existence, exten- sion, uniqueness and local character, and this relation is unique.

TL;DR: The structure of an o-minimal expansion of a densely ordered group and H be a pairwise disjoint collection of dense subsets of M such that ⋃ H is definably independent in M is studied.

TL;DR: It is shown that for any infinite countable group G and for any free Borel action G ↷ X there exists an equivariant class-bijective Borel map from X to the free part Free ( 2 G ) of the 2-shift G ↑ 2 G .

TL;DR: This paper introduces a formulation, involving towers, of symmetry over limit models for μ -superstable abstract elementary classes and uses this formulation to gain insight into the problem of the uniqueness oflimit models for categorical AECs.

TL;DR: Very general, though partly non-constructive, methods that cover all previous examples, and extend to an infinite family of modal logics are provided.

TL;DR: In this paper, the authors investigate regularity properties derived from tree-like forcing notions in the setting of generalized descriptive set theory on κ κ and 2 κ, for regular uncountable cardinals κ.

TL;DR: A parametrized construction of a Geometry of Interaction for Multiplicative Additive Linear Logic (MALL) in which proofs are represented by families of directed weighted graphs.

TL;DR: This theorem illuminates the structural side of such a dividing line and suggests a possible dividing line (μ-superstable + μ-symmetric) for abstract elementary classes without using extra set-theoretic assumptions or tameness.

TL;DR: In this paper, a deductive system is structurally complete if all of its admissible inference rules are derivable, i.e., a rule whose premise is not unifiable by any substitution.

TL;DR: This paper combines two approaches to the study of classification theory of AECs: studying non-forking frames without assuming the amalgamation property but assuming the existence of uniqueness triples and that of Grossberg and VanDieren assuming the non-splitting property and tameness.

TL;DR: It is shown that this category equivalent to that of Kleene–Kreisel continuous functionals has a fan functional and validates the uniform-continuity principle in these theories.

TL;DR: In this article, the authors use the language and tools available in model theory to redefine and clarify the rather involved notion of a special subvariety known from the theory of Shimura varieties (mixed and pure).

TL;DR: It is shown that all Zilber's countable strong exponential fields are computable exponential fields.

TL;DR: A finite support product of the Jensen minimal singleton forcing is made use to define a model in which Uniformization fails for a set with countable cross-sections.

TL;DR: It is shown that the automorphism groups of certain countable structures obtained using the Hrushovski amalgamation method are simple groups.

TL;DR: This paper investigates Rosser-type Henkin sentences, namely, sentences asserting their own provability in the sense of Rosser, and local reflection principles based on Rosser provability predicates, and solves the question raised by Shavrukov and gives a Rosser Provability predicate whose local reflection principle is strictly weaker than the usual one.

TL;DR: The goal is to investigate the termination analysis from the point of view of Reverse Mathematics by studying the strength of Podelski and Rybalchenko's Termination Theorem to extract some information about termination bounds.

TL;DR: In this paper, a hypersequent calculus with a cut rule is used to provide an alternative syntactic proof of the generation of the variety by the lattice-ordered group of automorphisms of the real number chain.

TL;DR: It is proved that the natural forcing for adding a large symmetric system of structures adds ℵ 1 -many reals but preserves CH.

TL;DR: In this article, the authors characterize model theoretic properties of the Urysohn sphere as a metric structure in continuous logic and show that it is SOP n for all n ≥ 3, but does not have the fully finite strong order property.

TL;DR: In this article, the lattice of reducts of the generic digraph (D, E ) is determined, where a structure M is a reduct of (D, E ) if it has domain D and all its ∅-definable relations are ∅definability relations of ( D, E ).

TL;DR: The notion of an analytically presented abstract elementary class (AEC) is introduced, which allows the formulation and proof of generalizations of these results to refer to Galois types rather than syntactic types.

TL;DR: It is shown that, for a wide class of theories U, transducibility coincides with interpretability over U and, for an even wider class, it coincides with Pi_1-conservativity over U.

TL;DR: A “slow” version of the hierarchy of uniform reflection principles over Peano Arithmetic (PA) is described and a new provably total function is introduced and it is deduced that the consistency ofPA plus slow reflection is provable inPA+Con(PA).

TL;DR: If all x have complexity K ( x ) ≥ k, D carries ≥i bits of information on each x where i + j ∼ k .

TL;DR: It is shown that the poset P, the algebra P / I G, the inverse of the right Green's pre-order 〈 Emb ( G ) , ⪯ R 〉 have the 2-localization property.

TL;DR: In this article, the authors generalize Hrushovski's Group Configuration Theorem to quasiminimal classes and show that a group can be found there if the pregeometry obtained from the bounded closure operator is non-trivial.

TL;DR: The key finding is that, in a continuous domain, bases correspond exactly to dense sets of one of these new topologies.