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1 results

THE IMPLICITLY CONSTRUCTIBLE UNIVERSE
MARCIA J. GROSZEK, JOEL DAVID HAMKINS
Journal:

The Journal of Symbolic Logic / Volume 84 / Issue 4 / December 2019

Published online by Cambridge University Press:

10 June 2019, pp. 1403-1421

Print publication:

December 2019
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We answer several questions posed by Hamkins and Leahy concerning the implicitly constructible universe Imp, which they introduced in [5]. Specifically, we show that it is relatively consistent with ZFC that $$Imp = \neg {\rm{CH}}$$, that $Imp \ne {\rm{HOD}}$, and that $$Imp \models V \ne Imp$$, or in other words, that $\left( {Imp} \right)^{Imp} \ne Imp$.