Premium
Ulm Classification of Analytic Equivalence Relations in Generic Universes
Author(s) -
Kanovei Vladimir
Publication year - 1998
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19980440302
Subject(s) - mathematics , countable set , equivalence relation , equivalence (formal languages) , mathematical proof , sigma , discrete mathematics , universe , binary relation , extension (predicate logic) , set (abstract data type) , binary number , pure mathematics , combinatorics , arithmetic , computer science , physics , geometry , quantum mechanics , astrophysics , programming language
We prove that if every real belongs to a set generic extension of L , then every Σ 1 1equivalence relation E on reals either admits a Δ 1 reduction to the equality on the set 2 < ω1 of all countable binary sequences, or the Vitali equivalence E 0 continuously embeds in E. The proofs are based on a topology generated by OD sets.