SEPARATING SUBVERSION FORCING AXIOMS

Abstract We study a family of variants of Jensen’s subcomplete forcing axiom , $\mathsf {SCFA,}$ and subproper forcing axiom , $\mathsf {SubPFA}$ . Using these, we develop a general technique for proving nonimplications 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.