The Axiom of Choice in the κ-Mantle

2024/03/14 by Andreas Lietz, Lietz, Andreas
Computer Science · Mathematics · #03E25 03E35 03E55 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2403.09015

openalex publication_date 2024/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Usuba has asked whether the κ-mantle, the intersection of all grounds that extend to V via a forcing of size <κ, is always a model of ZFC. We give a negative answers by constructing counterexamples where κ is a Mahlo cardinal, κ=ω₁ and where κ is the successor of a regular uncountable cardinal.

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