On    Σ  1  1   ‐complete equivalence relations on the generalized Baire space | Zendy

Hyttinen Tapani | Zendy; Kulikov Vadim | Zendy

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On Σ 1 1 ‐complete equivalence relations on the generalized Baire space

Author(s) -

Hyttinen Tapani,

Kulikov Vadim

Publication year - 2015

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.201200063

Subject(s) - mathematics , uncountable set , equivalence relation , undecidable problem , cardinality (data modeling) , isomorphism (crystallography) , baire space , congruence relation , relation (database) , equivalence (formal languages) , complete metric space , discrete mathematics , baire category theorem , pure mathematics , combinatorics , countable set , banach space , decidability , chemistry , database , computer science , crystal structure , data mining , crystallography

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 Σ 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 Σ 1 1 ‐complete (it is, if V = L , but can be forced not to be).

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