On \Sigma^1_1-complete Equivalence Relations on the Generalized Baire Space

Tapani Hyttinen; Vadim Kulikov

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arXiv · 1209.3932

On \Sigma^1_1-complete Equivalence Relations on the Generalized Baire Space

Tapani Hyttinen·Vadim Kulikov

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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).

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BibTeX RIS

Tapani Hyttinen, Vadim Kulikov. 2012-09-18. On \Sigma^1_1-complete Equivalence Relations on the Generalized Baire Space. https://arxiv.org/abs/1209.3932

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