Related papers: Locally compact groups and continuous logic

The classical Baldwin-Lachlan characterization of uncountably categorical theories is known to fail in continuous logic in that not every inseparably categorical theory has a strongly minimal set. Here we investigate these issues by…

We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…

We give a complete characterization of the locally compact groups that are non-elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting…

We develop the theory of ultracoproducts and weak containment for flows of arbitrary topological groups. This provides a nice complement to corresponding theories for p.m.p. actions and unitary representations of locally compact groups. For…

We study locally compact convergence groups, in particular the link between the convergence property and the Specker compactifications (a genaralization of the ends) of a group.

We consider (finitary, propositional) logics through the original use of Category Theory: the study of the "sociology of mathematical objects", aligning us with a recent, and growing, trend of study logics through its relations with other…

Let $k$ be a field. We characterize the group schemes $G$ over $k$, not necessarily affine, such that $\mathsf{D}_{\mathrm{qc}}(B_kG)$ is compactly generated. We also describe the algebraic stacks that have finite cohomological dimension in…

The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.

This paper focuses on the expressive power of disjunctive and normal logic programs under the stable model semantics over finite, infinite, or arbitrary structures. A translation from disjunctive logic programs into normal logic programs is…

We investigate intuitionistic modal logics with locally interpreted $\square$ and $\lozenge$. The basic logic LIK is stronger than constructive modal logic WK and incomparable with intuitionistic modal logic IK. We propose an axiomatization…

Given a multiplicatively closed subset $S$ of the integers, there exist Structure Theorems for $LC$ modules over the localization $\mathbb{Z}S^{-1}$ that are "similar" to those of $LCA$ groups. The most notable one is the 1st Theorem: Given…

We survey the legacy of L.G. Kov\'acs in linear group theory, with a particular focus on classification questions.

In this paper, we study aggregation rules with nontrivial symmetric classes of invariant sets (restricted domains), assuming that they, unlike others, have a logical nature. In the simplest case, we provide a complete classification of such…

This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…

Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…

We give an introduction to the Cayley-Abels graph for a totally disconnected, locally compact (tdlc) group. It is a generalization of the Cayley graph. We illustrate that on the one hand, Cayley-Abels graphs are useful tools to extend…

We consider model-theoretic properties related to the expressive power of three analogues of $L_{\omega_1, \omega}$ for metric structures. We give an example showing that one of these infinitary logics is strictly more expressive than the…

We use a novel type of epistemic logic, employing comparative knowledge assertions, to analyze the relative epistemic powers of individuals or groups of agents. Such comparative assertions can express that a group has the potential to…

Here, we classify Lie groups acting isometrically on compact Lorentz manifolds, and in particular we describe the geometric structure of compact homogeneous Lorentz manifolds.

We develop a unified approach to the classical Hopf Decomposition (also known as the conservative--dissipative decomposition) for actions of locally compact second countable groups. While the decomposition is well understood for free…