Notre Dame Journal of Formal Logic

Reducibility of Equivalence Relations Arising from Nonstationary Ideals under Large Cardinal Assumptions

David Asperó, Tapani Hyttinen, Vadim Kulikov, and Miguel Moreno

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Abstract

Working under large cardinal assumptions such as supercompactness, we study the Borel reducibility between equivalence relations modulo restrictions of the nonstationary ideal on some fixed cardinal κ. We show the consistency of Eλ-clubλ++,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλλ++ in the space (λ++)λ++, being continuously reducible to Eλ+-club2,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλ+λ++ in the space 2λ++. Then we show that for κ ineffable Ereg2,κ, the relation of equivalence modulo the nonstationary ideal restricted to regular cardinals in the space 2κ is Σ11-complete. We finish by showing that, for Π21-indescribable κ, the isomorphism relation between dense linear orders of cardinality κ is Σ11-complete.

Article information

Source
Notre Dame J. Formal Logic, Volume 60, Number 4 (2019), 665-682.

Dates
Received: 5 August 2017
Accepted: 18 July 2018
First available in Project Euclid: 14 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1568426586

Digital Object Identifier
doi:10.1215/00294527-2019-0024

Subjects
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05]
Secondary: 03C45: Classification theory, stability and related concepts [See also 03C48]

Keywords
large cardinals generalized Baire spaces equivalence relations

Citation

Asperó, David; Hyttinen, Tapani; Kulikov, Vadim; Moreno, Miguel. Reducibility of Equivalence Relations Arising from Nonstationary Ideals under Large Cardinal Assumptions. Notre Dame J. Formal Logic 60 (2019), no. 4, 665--682. doi:10.1215/00294527-2019-0024. https://projecteuclid.org/euclid.ndjfl/1568426586


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