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.
Citation
David Asperó. Tapani Hyttinen. Vadim Kulikov. Miguel Moreno. "Reducibility of Equivalence Relations Arising from Nonstationary Ideals under Large Cardinal Assumptions." Notre Dame J. Formal Logic 60 (4) 665 - 682, November 2019. https://doi.org/10.1215/00294527-2019-0024
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