Consistency of the Silver dichotomy in generalised Baire space
Sy-David Friedman
Fundamenta Mathematicae, Tome 227 (2014), p. 179-186 / Harvested from The Polish Digital Mathematics Library
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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 κκ 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 κκ for uncountable regular κ is however consistent (with GCH), assuming the existence of 0.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:282958 
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Sy-David Friedman. Consistency of the Silver dichotomy in generalised Baire space. Fundamenta Mathematicae, Tome 227 (2014) pp. 179-186. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm227-2-4/