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Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics…
In this note we introduce the concept of a quasi-finite complex. Next, we show that for a given countable and locally finite CW complex L the following conditions are equivalent: (i) L is quasi-finite. (ii) There exists a [L]-invertible…
Given a regular cardinal $\kappa$ such that $\kappa^{<\kappa}=\kappa$ (e.g., if the Generalized Continuum Hypothesis holds), we develop a proof system for classical infinitary logic that includes heterogeneous quantification (i.e., infinite…
In this work we study the decidability of a class of global modal logics arising from Kripke frames evaluated over certain residuated lattices, known in the literature as modal many-valued logics. We exhibit a large family of these modal…
A theorem of Nekrashevych and Sidki shows the Mealy Automata structures one can place on Z^m are parametrized by a family of matrices (called "1/2-integral") and a choice of residuation vector e in Z^m. While the impact of the chosen matrix…
This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with…
For each natural number $n$ we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater than $n$ and no strictly ascending chains. The case $n=0$ is the G\"odel-L\"ob…
We study an open question at the interplay between the classical and the dynamical Mordell-Lang conjectures in positive characteristic. Let $K$ be an algebraically closed field of positive characteristic, let $G$ be a finitely generated…
Let $ K / k $ be a purely inseparable extension of characteristic $ p> 0 $ and of finite size. We recall that $K/k$ is modular if for every $n \in \mathbb{N}$,$K^{p^n}$ and $k$ are $k\cap K^{p^ n}$-linearly disjoint. A natural…
We prove undecidability and pinpoint the place in the arithmetical hierarchy for commutative action logic, that is, the equational theory of commutative residuated Kleene lattices (action lattices), and infinitary commutative action logic,…
We present the notions of positively complete theory and general forms of amalgamation in the framework of positive logic. We explore the fundamental properties of positively complete theories and study the behaviour of companion theories…
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of…
In this paper the notion of Dirac structure in finite dimension is extended to the convenient setting. In particular, we introduce the notion of partial Dirac structure on convenient Lie algebroids and manifolds. We then look for those…
We describe several infinite series of rational conformal field theories whose conformal characters are modular units, i.e. which are modular functions having no zeros or poles in the upper complex half plane, and which thus possess simple…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
The Blok-Esakia theorem states that there is an isomorphism from the lattice of intermediate logics onto the lattice of normal extensions of Grzegorczyk modal logic. The extension for multi-conclusion consequence relations was obtained by…
We develop a unified algebraic and valuative theory of Lojasiewicz exponents for pairs of graded families and filtrations of ideals. Within this framework, local Lojasiewicz exponents, gradient exponents, and exponents at infinity are all…
Simply-connected manifolds of positive sectional curvature $M$ are speculated to have a rigid topological structure. In particular, they are conjectured to be rationally elliptic, i.e., all but finitely many homotopy groups are conjectured…
An algebraic proof is presented for the finite strong standard completeness of involutive uninorm logic with fixed point. The result may provide a first step towards settling the open standard completeness problem for involutive uninorm…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…