## Bulletin of Symbolic Logic

### Analytic equivalence relations and the forcing method

Jindřich Zapletal

#### Abstract

I describe several ways in which forcing arguments can be used to yield clean and conceptual proofs of nonreducibility, ergodicity and other results in the theory of analytic equivalence relations. In particular, I present simple Borel equivalence relations $E, F$ such that a natural proof of nonreducibility of $E$ to $F$ uses the independence of the Singular Cardinal Hypothesis at $\aleph_\omega$.

#### Article information

Source
Bull. Symbolic Logic, Volume 19, Issue 4 (2013), 473-490.

Dates
First available in Project Euclid: 5 January 2014

https://projecteuclid.org/euclid.bsl/1388953942

Digital Object Identifier
doi:10.2178/bsl.1904020

Mathematical Reviews number (MathSciNet)
MR3157161

Zentralblatt MATH identifier
1326.03061

Subjects
Primary: 03E40: Other aspects of forcing and Boolean-valued models

#### Citation

Zapletal, Jindřich. Analytic equivalence relations and the forcing method. Bull. Symbolic Logic 19 (2013), no. 4, 473--490. doi:10.2178/bsl.1904020. https://projecteuclid.org/euclid.bsl/1388953942