Consistency of the Silver dichotomy in generalised Baire space

• Autorzy: Sy-David Friedman
• Języki publikacji: EN

Abstrakty

EN

Silver's fundamental dichotomy in the classical theory of Borel reducibility states that any Borel (or even co-analytic) equivalence relation with uncountably many classes has a perfect set of classes. The natural generalisation of this to the generalised Baire space $κ^{κ}$ for a regular uncountable κ fails in Gödel's L, even for κ-Borel equivalence relations. We show here that Silver's dichotomy for κ-Borel equivalence relations in $κ^{κ}$ for uncountable regular κ is however consistent (with GCH), assuming the existence of $0^{#}$.

Kategorie tematyczne

• 03E55: Large cardinals
• 03E15: Descriptive set theory
• 03E45: Inner models, including constructibility, ordinal definability, and core models
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 227
• Numer: 2
• Strony: 179-186

Daty

wydano

2014

Twórcy

autor

Sy-David Friedman

• Kurt Gödel Research Center, University of Vienna, 1090 Wien, Austria

Identyfikatory

DOI

10.4064/fm227-2-4