English

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