[PDF] Top 20 Amenability, Countable Equivalence Relations, and Their Full Groups

... between equivalence relations stronger than being non-isomorphic is the non-existence of countable-to-one homomorphisms from one of them to the ...between countable equivalence ... See full document

... of amenability and coamenability for algebraic quantum groups in the sense of Van Daele ...implies amenability of its ...for amenability or coamenability are ... See full document

... amenable groups as exactly those groups Γ for which s Γ admits a non-trivial sequence of almost invariant ...that amenability of Γ is equivalent to every measure preserv- ing action of Γ being weakly ... See full document

... Keywords Convolution Operators, Locally Compact Groups, Abstract Harmonic Analysis, Amenable Groups 1. Introduction Let G be a locally compact group and H a closed subgroup, this paper is concerned with the ... See full document

... Because of the possibility to decompose a set into two fam- ilies of sets that, if rearranged properly, can form two sets as the initial one, we call these kind of sets paradoxical sets. We also say they bear a ... See full document

... We provide an abstract characterisation of ultra-amenability, similar to the concept of an ap- proximate diagonal, see [30, Section 2.2]. To do this, we need to first study how tensor products and ultrapowers ... See full document

... a countable Borel equivalence relation (X, E), generated by a countable Borel group action Γ y X, the measure-theoretic ergodic decomposition of E may be realized via the topological ergodic ... See full document

... case that one uses the semi-algebraic language (also called Macintyre’s language) from [55], but the results and method of this appendix differ in two important ways from the main body of the paper. Firstly, our method ... See full document

... Key words: equivalence relations, equivalence-equivalence, training-structure. r esumen En el presente estudio se investiga la influencia de la estructura de entrenamiento en la formación de ... See full document

... 1 equivalence relations with all ∆ 1 1 classes if there exists a Ramsey cardinal. After showing the positive answer follows from certain large cardinal principles, a natural question would be whether the ... See full document

... Theorem 1.2.2. (Harrington-Kechris-Louveau) If X is a Polish space and E is a Borel equivalence relation on X, then either E is smooth or E 0 6 B E. In fact, the Glimm-Effros dichotomy indicates something ... See full document

... using equivalence-equivalence relations (two equivalence relations related to each other) in a series of three ...on equivalence relations between arbitrary stimuli using ... See full document

... a countable generating partition and the sofic entropy h Σ G (X, µ) satisfies h Σ G (X, µ) = H(α) < ∞, then (X, µ) is isomorphic to a Bernoulli ...amenable groups factors of Bernoulli shifts are ... See full document

... 2 Statement of the main results The purpose of this section is to state the main theorem of this paper. A graph Γ is a set of vertices and undirected edges between those vertices. Two vertices of a graph are adjacent if ... See full document

... Articles appearing in the journal have been carefully and critically refereed under the responsibility of members of the Editorial Board. Only papers judged to be both significant and excellent are accepted for ... See full document

... an equivalence relation and we can restate the problem as a graph covering problem: We seek to cover the edges of a graph G with k equivalence subgraphs, ...an equivalence covering of G ...the ... See full document

... To repeat the first sentence more concretely, descriptive set theory concerns the study of definable sets in Polish spaces. Descriptive set theory is a major research area of set theory and can both be approached from ... See full document

... any countable graph. There are 2 ℵ 0 non-regular D -classes of the countable universal bipartite graph B such that the Sch¨ utzenberger group of H -classes within them are isomorphic to Aut ... See full document

... Also by Proposition 4.3, action type geometric Noetherianity and ac- tion type logic Noetherianity of representation does not depend on sub- variety Θ. The paper is organized as follows. We start with two auxiliary sec- ... See full document

... As mentioned in the Introduction, our construction is based on the proof of Whitehead [Wh, Theorem 13] that every countable CW-complex is homotopy equivalent to a locally finite complex of the same dimension. That ... See full document