Swan, Andrew W

Constructive theories usually have interesting metamathematical properties where explicit witnesses can be extracted from proofs of existential sentences. For relational theories, probably the most natural of these is the existence property, EP, sometimes referred to as the set existence property. This states that whenever (\exists x)\phi(x) is pro...

Caicedo, Xavier Iovino, José N.
Published in
Annals of Pure and Applied Logic

We study a class of [0,1]-valued logics. The main result of the paper is a maximality theorem that characterizes these logics in terms of a model-theoretic property, namely, an extension of the omitting types theorem to uncountable languages.

Higuchi, K. Kihara, T.
Published in
Annals of Pure and Applied Logic

Shlapentokh, Alexandra Videla, Carlos
Published in
Annals of Pure and Applied Logic

Higuchi, K. Kihara, T.
Published in
Annals of Pure and Applied Logic

Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify nonuniformly computable functions on Baire space from the viewpoint of learning theory and piecewise computability. For ...

Published in
Annals of Pure and Applied Logic

Solanki, Vinesh Sustretov, Dmitry Zilber, Boris
Published in
Annals of Pure and Applied Logic

A structure is associated with the quantum harmonic oscillator, over a fixed algebraically closed field F of characteristic 0, which is shown to be uncountably categorical. An analysis of definable sets is carried out, from which it follows that this structure is a Zariski geometry of dimension 1. It is non-classical in the sense that it is not int...

Solanki, Vinesh Sustretov, Dmitry Zilber, Boris
Published in
Annals of Pure and Applied Logic

Higuchi, K. Kihara, T.
Published in
Annals of Pure and Applied Logic

It is known that infinitely many Medvedev degrees exist inside the Muchnik degree of any nontrivial Π10 subset of Cantor space. We shed light on the fine structures inside these Muchnik degrees related to learnability and piecewise computability. As for nonempty Π10 subsets of Cantor space, we show the existence of a finite-Δ20-piecewise degree con...

Miller, Arnold W. Tsaban, Boaz Zdomskyy, Lyubomyr

We study the preservation of selective covering properties, including classic ones introduced by Menger, Hurewicz, Rothberger, Gerlits and Nagy, and others, under products with some major families of concentrated sets of reals. Our methods include the projection method introduced by the authors in an earlier work, as well as several new methods. So...