On large cardinals and generalized Baire spaces

2017/08/09 by Asperó, David, Hyttinen, Tapani, Kulikov, Vadim +1
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1708.02814

Abstract

Working under large cardinal assumptions, we study the Borel-reducibility between equivalence relations modulo restrictions of the non-stationary ideal on some fixed cardinal κ. We show the consistency of E^λ⁺⁺,λ⁺⁺_λ-club, the relation of equivalence modulo the non-stationary ideal restricted to S^λ⁺⁺_λ in the space (λ⁺⁺)^λ⁺⁺, being continuously reducible to E^2,λ⁺⁺_λ⁺-club, the relation of equivalence modulo the non-stationary ideal restricted to S^λ⁺⁺_λ⁺ in the space 2^λ⁺⁺. Then we show the consistency of E^2,κ_reg, the relation of equivalence modulo the non-stationary ideal restricted to regular cardinals in the space 2^κ, being Σ₁¹-complete. We finish by showing, for Π₂¹-indescribable κ, that the isomorphism relation between dense linear orders of cardinality κ is Σ₁¹-complete.

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