On nice equivalence relations on 2^\lambda
逻辑
2007-05-23 v1
摘要
The main question here is the possible generalization of the following theorem on ``simple'' equivalence relation on 2^omega to higher cardinals. Theorem: (1) Assume that: (a) E is a Borel 2-place relation on 2^omega, (b) E is an equivalence relation, (c) if eta, nu in 2^omega and (exists ! n)(eta(n) not= nu(n)), then eta, nu are not E --equivalent. Then there is a perfect subset of 2^omega of pairwise non E-equivalent members. (2) Instead of ``E is Borel'', ``E is analytic (or even a Borel combination of analytic relations)'' is enough. (3) If E is a Pi^1_2 relation which is an equivalence relation satisfying clauses (b)+(c) in V^Cohen, then the conclusion of (1) holds.
引用
@article{arxiv.math/0009064,
title = {On nice equivalence relations on 2^\lambda},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/0009064},
year = {2007}
}