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arXiv · 1812.06192

Well-Ordered Model Universes

Alon Navon
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Abstract

In this paper we show how to build a model of $ZFC$ such that all its inner models satisfying the Axiom of Choice are well-ordered with respect to inclusion, and that said ordering is of arbitrary height (including possibly $Ord$ high). We do this by iterating $κ$-Sacks forcing for ever-increasing $κ$, while showing that such forcings do not add any unexpected intermediate inner models.

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Alon Navon. 2018-12-14. Well-Ordered Model Universes. https://arxiv.org/abs/1812.06192

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