DEFINABLE MINIMAL COLLAPSE FUNCTIONS AT ARBITRARY PROJECTIVE LEVELS
Vladimir Grigor'evich Kanovei, Vassily Lyubetsky · Journal of Symbolic Logic · 2019
Abstract Using a nonLaver modification of Uri Abraham’s minimal $\Delta _3^1$ collapse function, we define a generic extension $L[a]$ by a real a, in which, for a given $n \ge 3$ , $\left\{ a \right\}$ is a lightface $\Pi _n^1 $ singleton, a effectively codes a cofinal map $\omega \to \omega _1^L $ minimal over L, while every $\Sigma _n^1 $ set $X \subseteq \omega $ is still constructible.