Presents Results from a Very Active Area of ResearchExploring an active area of
mathematics that studies the complexity of equivalence relations and classification …

RI Grigorchuk, VV Nekrashevych, VI Sushchanskii, “Automata, Dynamical Systems, and
Groups”, Dynamical systems, automata, and infinite groups, Collected papers, Trudy Mat. Inst …

This volume provides a self-contained introduction to some topics in orbit equivalence
theory, a branch of ergodic theory. The first two chapters focus on hyperfiniteness and …

Actions of Polish groups are ubiquitous in mathematics. In certain branches of ergodic
theory and functional analysis, one finds a systematic study of the group of measure …

" The subject of this book is the study of ergodic, measure preserving actions of countable
discrete groups on standard probability spaces. It explores a direction that emphasizes a …

COUNTABLE BOREL EQUIVALENCE RELATIONS Page 1 May 2, 2002 17:8 WSPC/153-JML
00013 Journal of Mathematical Logic, Vol. 2, No. 1 (2002) 1–80 c World Scientific Publishing …

Whenever a structure with a particularly interesting computability-theoretic property is found,
it is natural to ask whether similar examples can be found within well-known classes of …

We announce two new dichotomy theorems for Borel equivalence relations, and present the
results in context by giving an overview of related recent developments. § 1. Introduction. For …

We study the classification problem of Polish metric spaces up to isometry and the isometry
groups of Polish metric spaces. In the framework of the descriptive set theory of definable …

We study connections between distributed local algorithms, finitary factors of iid processes,
and descriptive combinatorics in the context of regular trees. We extend the Borel …