Varia: Ideals and Equivalence Relations, betaversion
Abstract
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 Banachinduced 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 Rosendal's proof that Borel ideals are cofinal within Borel equivalences of general form.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2006
 arXiv:
 arXiv:math/0610988
 Bibcode:
 2006math.....10988K
 Keywords:

 Mathematics  Logic;
 03E15
 EPrint:
 Borel equivalence relations: structure and classification, University Lectures series of the AMS, 2008. Monograph 9780821844533