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DEFINABLE MINIMAL COLLAPSE FUNCTIONS AT ARBITRARY PROJECTIVE LEVELS

Published online by Cambridge University Press:  14 March 2019

VLADIMIR KANOVEI
Affiliation:
IITP RAS, BOLSHOY KARETNY 19 BUILD. 1 MOSCOW 127051, RUSSIAE-mail: kanovei@googlemail.com
VASSILY LYUBETSKY
Affiliation:
IITP RAS, BOLSHOY KARETNY 19 BUILD. 1 MOSCOW 127051, RUSSIAE-mail: lyubetsk@iitp.ru

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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Copyright
Copyright © The Association for Symbolic Logic 2019 

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DEFINABLE MINIMAL COLLAPSE FUNCTIONS AT ARBITRARY PROJECTIVE LEVELS
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