PFA AND THE DEFINABILITY OF THE NONSTATIONARY IDEAL
Stefan Hoffelner, Paul Larson, RALF SCHINDLER, Liuzhen Wu · Journal of Symbolic Logic · 2025
Abstract We produce, relative to a backslash textsf upper Z upper F upper C $\textsf {ZFC}$ \textsf Z F C model with a supercompact cardinal, a backslash textsf upper Z upper F upper C $\textsf {ZFC}$ \textsf Z F C model of the Proper Forcing Axiom in which the nonstationary ideal on omega 1 $\omega _1$ ω 1 is upper Pi 1 $\Pi _1$ Π 1 -definable in a parameter from upper H Subscript normal first transfinite cardinal 2 $H_{\aleph _2}$ H ℵ 2 .