• Corpus ID: 117282309

Varia: Ideals and Equivalence Relations, beta-version

@article{Kanovei2006VariaIA,
  title={Varia: Ideals and Equivalence Relations, beta-version},
  author={Vladimir Kanovei},
  journal={arXiv: Logic},
  year={2006}
}
  • V. Kanovei
  • Published 31 October 2006
  • Mathematics
  • arXiv: Logic
We present a selection of basic results on Borel reducibility of Borel ideals and equivalence relations, especially those with comparably short proofs. The focal point are reducibility/irreducibility results related to some special equivalences like $E_0, E_1, E_2, E_3, E_\infty, Z_0,$ and Banach-induced equivalences $l_p,$ in particular several dichotomy theorems. The bulk of results included in the book were obtained in the 1990s, but some rather recent theorems are presented as well, like… 

References

SHOWING 1-10 OF 40 REFERENCES
Recent developments in the theory of Borel reducibility
Let E_0 be the Vitali equivalence relation and E_3 the product of countably many copies of E_0. Two new dichotomy theorems for Borel equivalence relations are proved. First, for any Borel
A confinal family of equivalence relations and Borel ideals generating them
An increasing θ1-sequence of Borel equivalence relations on a Polish space that is cofinal (in the sense of Borel reducibility) in the family of all Borel equivalence relations is defined as a
The structure of hy-per nite Borel equivalence relations
We study the structure of the equivalence relations induced by the orbits of a single Borel automorphism on a standard Borel space. We show that any two such equivalence relations which are not
The classification of hypersmooth Borel equivalence relations
This paper is a contribution to the study of Borel equivalence relations in standard Borel spaces, i.e., Polish spaces equipped with their Borel structure. A class of such equivalence relations which
BOREL AND BAIRE REDUCIBILITY
The Borel reducibility theory of Polish equivalence relations, at least in its present form, was initiated in [FS89]. There is now an extensive literature on this topic, including fundamental work on
Borel Equivalence Relations Induced by Actions of the Symmetric Group
We consider Borel equivalence relations E induced by actions of the infinite symmetric group, or equivalently the isomorphism relation on classes of countable models of bounded Scott rank. We relate
On the reducibility order between borel equivalence relations
Publisher Summary This chapter focuses on the reducibility order between Borel equivalence relations. An equivalence relation E on a set X is a Borel equivalence relation if both X and E are Borel,
Linear algebraic groups and countable Borel equivalence relations
This paper is a contribution to the study of Borel equivalence relations on standard Borel spaces (i.e., Polish spaces equipped with their Borel structure). In mathematics one often deals with
Cofinal families of Borel equivalence relations and quasiorders
  • C. Rosendal
  • Mathematics, Computer Science
    Journal of Symbolic Logic
  • 2005
TLDR
Several Borel equivalence relations, among them Lipschitz isomorphism of compact metric spaces, are shown to be Kσ complete.
A Glimm-Effros dichotomy for Borel equivalence relations
A basic dichotomy concerning the structure of the orbit space of a transformation group has been discovered by Glimm [G12] in the locally compact group action case and extended by Effros [E 1, E2] in
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