Separating Subversion Forcing Axioms

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 ${\mathsf{MA}}^{+}(\ddot{I}ƒ$-closed$)$ and $\mathsf{SubPFA}$ does not imply Martin's Maximum.

19 pages, 1 figure, updated version addresses many helpful comments of the anonymous referee which helped clean up the text and clarify both the exposition and the proofs