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arXiv · 2308.16276

Separating Subversion Forcing Axioms

Hiroshi Sakai·Corey Bacal Switzer
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Abstract

We study a family of variants of Jensen's\emph{subcomplete forcing axiom}, $\mathsf{SCFA}$ and \emph{subproper forcing axiom}, $\mathsf{SubPFA}$. Using these we develop a general technique for proving non-implications of $\mathsf{SCFA}$, $\mathsf{SubPFA}$ and their relatives and give several applications. For instance we show that $\mathsf{SCFA}$ does not imply $\mathsf{MA}^+(\sigma$-closed$)$ and $\mathsf{SubPFA}$ does not imply Martin's Maximum.

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BibTeXRIS

Hiroshi Sakai, Corey Bacal Switzer. 2023-08-30. Separating Subversion Forcing Axioms. https://doi.org/10.1017/jsl.2025.10101

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