On \Sigma^1_1-complete Equivalence Relations on the Generalized Baire Space
Logic
2012-09-19 v1
Abstract
Working with uncountable structures of fixed cardinality, we investigate the complexity of certain equivalence relations and show that if V = L, then many of them are \Sigma^1_1-complete, in particular the isomorphism relation of dense linear orders. Then we show that it is undecidable in ZFC whether or not the isomorphism relation of a certain well behaved theory (stable, NDOP, NOTOP) is \Sigma^1_1-complete (it is, if V = L, but can be forced not to be).
Keywords
Cite
@article{arxiv.1209.3932,
title = {On \Sigma^1_1-complete Equivalence Relations on the Generalized Baire Space},
author = {Tapani Hyttinen and Vadim Kulikov},
journal= {arXiv preprint arXiv:1209.3932},
year = {2012}
}
Comments
22 pages