Reducibility of equivalence relations arising from nonstationary ideals under large cardinal assumptions

David Asperó, Tapani Hyttinen, Vadim Kulikov, Miguel Moreno

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 E λCC;λCC λ-club , the relation of equivalence modulo the nonstationary ideal restricted to SλCC λ in the space .λCC/λCC, being continuously reducible to E 2;λCC λC-club, the relation of equivalence modulo the nonstationary ideal restricted to SλCC λC in the space 2λCC. Then we show that for κ ineffable E 2;κ reg , the relation of equivalence modulo the nonstationary ideal restricted to regular cardinals in the space 2κ is ?11 -complete. We finish by showing that, for ?12 -indescribable κ, the isomorphism relation between dense linear orders of cardinality κ is ?11 -complete.

Original languageEnglish
Pages (from-to)665-682
Number of pages18
JournalNotre Dame Journal of Formal Logic
Volume60
Issue number4
DOIs
StatePublished - 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 Duke University Press. All rights reserved.

Keywords

  • Equivalence relations
  • Generalized Baire spaces
  • Large cardinals

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