Reducibility of equivalence relations arising from non-stationary ideals under large cardinal assumptions

David Aspero, Tapani Hyttinen, Vadim Kulikov, Miguel Moreno

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
16 Downloads (Pure)

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 \kappa. We show the consistency of E^{\lambda^{++},\lambda^{++}}_{\lambda\text{-club}}, the relation of equivalence modulo the non-stationary ideal restricted to S^{\lambda^{++}}_\lambda in the space (\lambda^{++})^{\lambda^{++}}, being continuously reducible to E^{2,\lambda^{++}}_{\lambda^+\text{-club}}, the relation of equivalence modulo the non-stationary ideal restricted to S^{\lambda^{++}}_{\lambda^+} in the space 2^{\lambda^{++}}. Then we show that for \kappa ineffable E^{2, \kappa}_{\text{reg}}, the relation of equivalence modulo the non-stationary ideal restricted to regular cardinals in the space 2^{\kappa}, is \Sigma^1_1-complete. We finish by showing, for \Pi_2^1-indescribable \kappa, that the isomorphism relation between dense linear orders of cardinality \kappa is \Sigma^1_1-complete.
Original languageEnglish
Pages (from-to)665-682
Number of pages18
JournalNotre Dame Journal for Formal Logic
Volume60
Issue number4
Early online date14 Sep 2019
DOIs
Publication statusPublished - Nov 2019

Cite this