Ulm Classification of Analytic Equivalence Relations in Generic Universes | Zendy

Kanovei Vladimir | Zendy

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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.

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