F_σ equivalence relations and Laver forcing

2012/11/26 by Michal Doucha, Doucha, Michal
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Functional Equations Stability Results #Logic (math.LO) #Rings, Modules, and Algebras #math.CO #math.LO

paper · pdf · doi:10.48550/arxiv.1211.5959

arxiv created 2012/11/26 · openalex publication_date 2012/11/26 · arxiv updated 2012/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Equivalence Relations Which Are Borel Somewhere
• The Borel Ramsey properties for countable Borel equivalence relations
• When an Equivalence Relation with All Borel Classes will be Borel Somewhere?
• Laver Trees in the Generalized Baire Space
• Forcing constructions and countable Borel equivalence relations