On the existence of large antichains for definable quasi-orders

Journal of Symbolic Logic 85 (1):103-108 (2020)
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Abstract

We simultaneously generalize Silver’s perfect set theorem for co-analytic equivalence relations and Harrington-Marker-Shelah’s Dilworth-style perfect set theorem for Borel quasi-orders, establish the analogous theorem at the next definable cardinal, and give further generalizations under weaker definability conditions.

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Benjamin Miller
University of Illinois, Urbana-Champaign

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