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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 , isomorphism (crystallography) , cardinality (data modeling) , baire space , equivalence (formal languages) , relation (database) , borel equivalence relation , congruence relation , discrete mathematics , pure mathematics , space (punctuation) , countable set , decidability , computer science , chemistry , database , probability measure , borel measure , crystal structure , data mining , crystallography , operating system
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).