On Σ¹₁-complete Equivalence Relations on the Generalized Baire Space

2012/09/18 by Tapani Hyttinen, Hyttinen, Tapani, Vadim Kulikov +1
Computer Science · Mathematics · #03C55 #03E47 #Advanced Algebra and Logic #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1209.3932

openalex publication_date 2012/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Σ¹₁-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 Σ¹₁-complete (it is, if V = L, but can be forced not to be).

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