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arXiv · 2102.11666

The Slicing Axioms

Ziemowit Kostana·Saharon Shelah
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Abstract

We introduce the family of axioms, denoted $\operatorname{Slice}_\kappa$, that claim the existence of strictly increasing decompositions of the form $$2^{\delta}=\bigcup_{\alpha<\kappa} 2^{\delta}\cap M_\alpha,$$ where $\delta<\kappa$, and $\{M_\alpha|\; \alpha<\kappa\}$ is a $\subseteq$-increasing sequence of transitive models of set theory. We study compatibility of these axioms with versions of Martin's Axiom, and in particular show that $\operatorname{Slice}$ is compatible only with some very weak form of $MA$.

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BibTeXRIS

Ziemowit Kostana, Saharon Shelah. 2021-02-23. The Slicing Axioms. https://arxiv.org/abs/2102.11666

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