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Choice principles in local mantles

2020/06/01 by Farmer Schlutzenberg, Schlutzenberg, Farmer
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #math.LO #msc:03E25 #msc:03E45 #msc:03E55

paper · pdf · doi:10.48550/arxiv.2006.01119

19 pages. This version: Corrected some false statements (which were not used anywhere; see Footnotes 3, 7, 11, 13), in particular a statement falsely attributed to Usuba (see Footnote 3). Removed what was previously section 4, for inclusion in a separate paper. Improved exposition and made other minor edits

arxiv created 2020/12/20 · arxiv updated 2020/12/22

Abstract

Assume ZFC. Let κ be a cardinal. A <κ-ground is a transitive proper class W modelling ZFC and such that V is a generic extension of W via a forcing ℙ∈ W of cardinality <κ. The κ-mantle is the intersection of all <κ-grounds. We prove that certain partial choice principles in the κ-mantle are the consequence of κ being inaccessible/weakly compact, and some other related facts.

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