Mathematics > Logic
[Submitted on 10 Oct 2018 (v1), last revised 30 Oct 2018 (this version, v2)]
Title:Equivalence of generics
View PDFAbstract:Given a countable transitive model of set theory and a partial order contained in it, there is a natural countable Borel equivalence relation on generic filters over the model; two are equivalent if they yield the same generic extension. We examine the complexity of this equivalence relation for various partial orders, with particular focus on Cohen and random forcing. We prove, amongst other results, that the former is an increasing union of countably many hyperfinite Borel equivalence relations, while the latter is neither amenable nor treeable.
Submission history
From: Iian Smythe [view email][v1] Wed, 10 Oct 2018 18:48:42 UTC (21 KB)
[v2] Tue, 30 Oct 2018 15:08:46 UTC (21 KB)
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