Related papers: An elementary approach to sofic equivalence relati…
We study a positive-definite function associated to a measure-preserving equivalence relation on a standard probability space and use it to measure quantitatively the proximity of subequivalence relations. This is combined with a recent…
We show that the intuitionistic first-order theory of equality has continuum many complete extensions. We also study the Vitali equivalence relation and show there are many intuitionistically precise versions of it.
Given the large class of groups already known to be sofic, there is seemingly a shortfall in results concerning their permanence properties. We address this problem for wreath products, and in particular investigate the behaviour of more…
A group is sofic when every finite subset can be well approximated in a finite symmetric group. No example of a non-sofic group is known. Higman's group, which is a circular amalgamation of four copies of the Baumslag--Solitar group, is a…
We give the following characterization of sofic (weakly sofic) groups: a group $G$ is sofic (weakly sofic) if and only if any system of equations solvable in any alternating group (any finite group) is solvable over $G$.
One of the longstanding problems in universal algebra is the question of which finite lattices are isomorphic to the congruence lattices of finite algebras. This question can be phrased as which finite lattices can be represented as…
This note studies the existence of quotients by finite set theoretic equivalence relations. May 18: Substantial revisions with a new appendix by C. Raicu
In a previous paper the authors developed an operator-algebraic approach to Lewis Bowen's sofic measure entropy that yields invariants for actions of countable sofic groups by homeomorphisms on a compact metrizable space and by…
We generalise the notion of separable equivalence, originally presented by Linckelmann (2011), to an equivalence relation on additive categories. We use this generalisation to show that from an initial equivalence between two algebras we…
Motivated by classification, up to order isomorphism, of some dense subgroups of Euclidean space that are free of minimal rank, we obtain apparently new invariants for an equivalence relation (intermediate between Hermite and Smith) on…
Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other,…
A specialization semilattice is a semilattice together with a coarser preorder satisfying a compatibility condition. We show that the category of specialization semilattices is isomorphic to the category of semilattices with a congruence,…
In this paper we investigate a relationship between fully k-rotundity properties, uniform K-monotonicity properties, reflexivity and K-order continuity in a symmetric spaces E. We also answer a crucial question whether fully k-rotundity…
Let $G$ be a sofic group, and let $\Sigma = (\sigma_n)_{n\geq 1}$ be a sofic approximation to it. For a probability-preserving $G$-system, a variant of the sofic entropy relative to $\Sigma$ has recently been defined in terms of sequences…
In this note we study countable subgroups of the full group of a measure preserving equivalence relation. We provide various constraints on the group structure, the nature of the action, and on the measure of fixed point sets, that imply…
We define an equivalence relation on periodic continued fractions with partial quotients in a ring $\mathcal{O} \subseteq \mathbf{C}$, a group law on these equivalence classes, and a map from these equivalence classes to matrices in…
We introduce the notion of soficity for locally compact groups and list a number of open problems.
We introduce an equivalence relation, called cobordism, for words and study cobordism invariants of words inspired by methods of low-dimensional topology.
We take the first steps towards a better understanding of continuous orbit equivalence, i.e., topological orbit equivalence with continuous cocycles. First, we characterise continuous orbit equivalence in terms of isomorphisms of C*-crossed…
Various versions of the classical definitions of (one- and twosided) almost periodicity for functions on groups with values in a uniform space are formulated and their equivalence is shown.