On Borel groups
نویسندگان
چکیده
منابع مشابه
Borel Whitehead Groups
We investigate the Whiteheadness of Borel abelian groups (א1-free, without loss of generality as otherwise this is trivial). We show that CH (and even WCH) implies any such abelian group is free, and always א2-free. 1998 Mathematics Subject Classification 03C60, 03E15, 20K20.
متن کاملBorel Subgroups of Polish Groups
We study three classes of subgroups of Polish groups: Borel subgroups, Polishable subgroups, and maximal divisible subgroups. The membership of a subgroup in each of these classes allows one to assign to it a rank, that is, a countable ordinal, measuring in a natural way complexity of the subgroup. We prove theorems comparing these three ranks and construct subgroups with prescribed ranks. In p...
متن کاملIsomorphism of Borel Full Groups
Suppose that G and H are Polish groups which act in a Borel fashion on Polish spaces X and Y . Let EX G and E Y H denote the corresponding orbit equivalence relations, and [G] and [H] the corresponding Borel full groups. Modulo the obvious counterexamples, we show that [G] ∼= [H] ⇔ EX G ∼=B EY H .
متن کاملBorel Actions of Polish Groups
We show that a Borel action of a Polish group on a standard Borel space is Borel isomorphic to a continuous action of the group on a Polish space, and we apply this result to three aspects of the theory of Borel actions of Polish groups: universal actions, invariant probability measures, and the Topological Vaught Conjecture. We establish the existence of universal actions for any given Polish ...
متن کاملUniversal Borel Actions of Countable Groups
If the countable group G has a nonabelian free subgroup, then there exists a standard Borel G-space such that the corresponding orbit equivalence relation is countable universal. In this paper, we will consider the question of whether the converse also holds.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1990
ISSN: 0166-8641
DOI: 10.1016/0166-8641(90)90105-b