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

Aspero, David, Kulikov, Vadim, Hyttinen, Tapani and Moreno, Miguel (2018) Reducibility of equivalence relations arising from non-stationary ideals under large cardinal assumptions. Notre Dame Journal for Formal Logic. (In Press)

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    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.

    Item Type: Article
    Faculty \ School: Faculty of Science > School of Mathematics
    Depositing User: LivePure Connector
    Date Deposited: 16 Jan 2019 09:30
    Last Modified: 09 Apr 2019 14:04
    URI: https://ueaeprints.uea.ac.uk/id/eprint/69586
    DOI:

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