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DEFINABLE MINIMAL COLLAPSE FUNCTIONS AT ARBITRARY PROJECTIVE LEVELS

  • VLADIMIR KANOVEI (a1) and VASSILY LYUBETSKY (a2)

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.

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Keywords

DEFINABLE MINIMAL COLLAPSE FUNCTIONS AT ARBITRARY PROJECTIVE LEVELS

  • VLADIMIR KANOVEI (a1) and VASSILY LYUBETSKY (a2)

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