Related papers: An elementary approach to sofic equivalence relati…
We show that there exists a class of symbolic subshifts which realizes all Choquet simplices as simplices of invariant measures and the conjugacy relation on that class is hyperfinite.
We initiate the study of reducts of relational structures up to primitive positive interdefinability: After providing the tools for such a study, we apply these tools in order to obtain a classification of the reducts of the logic of…
We introduce an equivalence relation on the space $W^{1,1}(\Omega;{\mathbb S}^1)$ which classifies maps according to their "topological singularities". We establish sharp bounds for the distances (in the usual sense and in the Hausdorff…
We investigate relative holomorphic connections on a principal bundle over a family of compact complex manifolds. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic principal bundle over…
We exhibit two relation algebra atom structures such that they are elementarily equivalent but their term algebras are not. This answers Problem 14.19 in the book Hirsch, R. and Hodkinson, I., "Relation Algebras by Games", North-Holland,…
Two new notions of equivalence for representations of a Toeplitz algebra $\mathcal{E}_n$, $n<\infty$, on a common Hilbert space are defined. Our main results apply to $C^*$-dynamics and the conjugacy of certain $*$-endomorphisms. One…
We show that the category of partial comodules over a Hopf algebra $H$ is comonadic over ${\sf Vect}_k$ and provide an explicit construction of this comonad using topological vector spaces. The case when $H$ is finite dimensional is treated…
We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…
On a finite structure, the polymorphism invariant relations are exactly the primitively positively definable relations. On infinite structures, these two sets of relations are different in general. Infinitary primitively positively…
There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This…
In this paper we propose a definition of a recurrence relation homomorphism and illustrate our definition with a few examples. We then define the period of a k-th order of linear recurrence relation and deduce certain preliminary results…
In the first part of this survey, we present classical notions arising in combinatorics on words: growth function of a language, complexity function of an infinite word, pattern avoidance, periodicity and uniform recurrence. Our…
In this paper, we prove a criterion of elementary equivalence of stable linear groups over fields of characteristic two.
We introduce the notion of topological entropy of a formal languages as the topological entropy of the minimal topological automaton accepting it. Using a characterization of this notion in terms of approximations of the Myhill-Nerode…
We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.
We study approximate equivalence relations up to commensurability, in the presence of a definable measure. As a basic framework, we give a presentation of probability logic based on continuous logic. Hoover's normal form is valid here; if…
Various frameworks that generalise the notion of contextuality in theories of physics have been proposed; one is the sheaf-theoretic approach by Abramsky and Brandenburger; an other is the equivalence-based approach by Spekkens. We show…
Poincar\'e series of $p$-adic, definable equivalence relations have been studied in various cases since Igusa's and Denef's work related to counting solutions of polynomial equations modulo $p^n$ for prime $p$. General semi-algebraic…
In this paper we prove a sufficient condition for the existence of matchings in arbitrary groups and its linear analogue, which lead to some generalizations of the existing results in the theory of matchings in groups and central extensions…
This is a short survey of amenable equivalence relations.