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