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arXiv · 2403.09015

The Axiom of Choice in the $\kappa$-Mantle

Andreas Lietz
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Abstract

Usuba has asked whether the $\kappa$-mantle, the intersection of all grounds that extend to $V$ via a forcing of size ${<}\kappa$, is always a model of ZFC. We give a negative answers by constructing counterexamples where $\kappa$ is a Mahlo cardinal, $\kappa=\omega_1$ and where $\kappa$ is the successor of a regular uncountable cardinal.

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Andreas Lietz. 2024-03-14. The Axiom of Choice in the $\kappa$-Mantle. https://arxiv.org/abs/2403.09015

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