$F_σ$ equivalence relations and Laver forcing
Year: 2012
Type: preprint
Abstract: 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. Here we prove that equivalence relations Borel reducible to an equivalence relation on $2^ω$ given by some $F_σ$ $P$-ideal on $ω$ can be canonized to the full equivalence relation or to the identity relation. This has several corollaries, e.g. Silver type dichotomy for the Laver ideal and equivalences Borel reducible to equivalence relations given by $F_σ$ $P$-ideals.
Source: arXiv (Cornell University)
Author: Doucha, Michal
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394641424