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Abelian pro‐countable groups and non‐Borel orbit equivalence relations
Author(s) -
Malicki Maciej
Publication year - 2016
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201500064
Subject(s) - mathematics , abelian group , borel equivalence relation , countable set , equivalence relation , polish space , orbit (dynamics) , elementary abelian group , second countable space , non abelian group , pure mathematics , topological group , equivalence (formal languages) , discrete mathematics , combinatorics , topology (electrical circuits) , borel measure , mathematical analysis , probability measure , separable space , engineering , aerospace engineering
We study topological groups that can be defined as Polish, pro‐countable abelian groups, as non‐archimedean abelian groups or as quasi‐countable abelian groups, i.e., Polish subdirect products of countable, discrete groups, endowed with the product topology. We characterize tame groups in this class, i.e., groups all of whose continuous actions on a Polish space induce a Borel orbit equivalence relation, and relatively tame groups, i.e., groups all of whose diagonal actions α × β induce a Borel orbit equivalence relation, provided that α , β are continuous actions inducing Borel orbit equivalence relations.