Related papers: Realizing realizability results with classical con…

We examine the interplay between projectivity (in the sense that was introduced by S.~Ghilardi) and uniform post-interpolant for the classical and intuitionistic propositional logic. More precisely, we explore whether a projective…

Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we…

Order types are a well known abstraction of combinatorial properties of a point set. By Mn\"ev's universality theorem for each semi-algebraic set $V$ there is an order type with a realization space that is \emph{stably equivalent} to $V$.…

We develop contractive finite dimensional realizations for rational matrix functions of one variable on domains that are not simply connected, such as the annulus. The proof uses multivariable contractive realization results as well as…

We contribute to the knowledge of the quantifier completions and their applications by using the language of doctrines. This algebraic presentation allows us to properly analyse the behaviour of the existential and universal quantifiers. We…

We study the existence of stable matchings when agents have choice correspondences instead of preference relations. We extend the framework of \cite{chambers2017choice} by weakening the path independence assumption. For many-to-many…

We discuss the connections between the failure of the axiom of choice in set theory, and certain model-theoretic structures with enough symmetry.

We present a sequent calculus for abstract focussing, equipped with proof-terms: in the tradition of Zeilberger's work, logical connectives and their introduction rules are left as a parameter of the system, which collapses the synchronous…

We introduce a new class of extensions of terms that consists in navigation strategies and insertion of contexts. We introduce an operation of combination on this class which is associative, admits a neutral element and so that each…

In the first part of this article, we complete the program announced in the preliminary note [8] by proving a conjecture presented in [9] that states the equivalence of contractibility and p_{1}-stability for generalized spaces of formal…

In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…

We consider the problem of determining whether a set of primes, or, more generally, prime ideals in a number field, can be realized as a finite union of residue classes, or of Frobenius conjugacy classes. We give criteria for a set to be…

To each prime ideal in a polynomial ring over a field we associate an algebraic matroid and show that it is preserved under tropicalization. This gives a necessary condition for a tropical variety to be set-theoretically realizable from a…

Crawford's et al. (2021) article on estimation of discrete choice models with unobserved or latent consideration sets, presents a unified framework to address the problem in practice by using "sufficient sets", defined as a combination of…

In 1990 J-L. Krivine introduced the notion of storage operators. They are $\lambda$-terms which simulate call-by-value in the call-by-name strategy and they can be used in order to modelize assignment instructions. J-L. Krivine has shown…

By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with…

We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…

We study the LTL model-checking in possibilistic Kripke structure using possibility measure. First, the notion of possibilistic Kripke structure and the related possibility measure are introduced, then model-checking of reachability and…

We propose a theory of learning aimed to formalize some ideas underlying Coquand's game semantics and Krivine's realizability of classical logic. We introduce a notion of knowledge state together with a new topology, capturing finite…

We consider the problem of sequential prediction and provide tools to study the minimax value of the associated game. Classical statistical learning theory provides several useful complexity measures to study learning with i.i.d. data. Our…