Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 60, Number 4 (2019), 665-682.
Reducibility of Equivalence Relations Arising from Nonstationary Ideals under Large Cardinal Assumptions
David Asperó, Tapani Hyttinen, Vadim Kulikov, and Miguel Moreno
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 . We show the consistency of , the relation of equivalence modulo the nonstationary ideal restricted to in the space , being continuously reducible to , the relation of equivalence modulo the nonstationary ideal restricted to in the space . Then we show that for ineffable , the relation of equivalence modulo the nonstationary ideal restricted to regular cardinals in the space is -complete. We finish by showing that, for -indescribable , the isomorphism relation between dense linear orders of cardinality is -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
Mathematical Reviews number (MathSciNet)
MR4019866
Zentralblatt MATH identifier
07167762
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