F-sigma equivalence relations and Laver forcing

0433873 - MÚ 2015 RIV US eng J - Článek v odborném periodiku
Doucha, Michal
F-sigma equivalence relations and Laver forcing.
Journal of Symbolic Logic. Roč. 79, č. 2 (2014), s. 644-653. ISSN 0022-4812. E-ISSN 1943-5886
Grant CEP: GA AV ČR IAA100190902
Institucionální podpora: RVO:67985840
Klíčová slova: Borel equivalence relations * Laver ideal * canonical Ramsey theorem
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.541, rok: 2014
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9287231&fileId=S0022481213000327

Following the topic of the book Canonical Ramsey Theory on Polish Spaces by V. Kanovei, M. Sabok, and J. Zapletal we study Borel equivalences on Laver trees. We prove that equivalence relations Borel reducible to an equivalence relation on 2(omega) given by some F-sigma P-ideal on omega can be canonized to the full equivalence relation or to the identity relation. This has several consequences, e.g., Silver type dichotomy for the Laver ideal and equivalences Borel reducible to equivalence relations given by F-sigma P-ideals.
Trvalý link: http://hdl.handle.net/11104/0238075