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THE IMPLICITLY CONSTRUCTIBLE UNIVERSE

Published online by Cambridge University Press:  10 June 2019

MARCIA J. GROSZEK  and
JOEL DAVID HAMKINS
MARCIA J. GROSZEK
Affiliation:
DEPARTMENT OF MATHEMATICS DARTMOUTH COLLEGE 6188 KEMENY HALL HANOVER, NY03755-3551, USA E-mail: [email protected]
JOEL DAVID HAMKINS
Affiliation:
FACULTY OF PHILOSOPHY UNIVERSITY COLLEGE, OXFORD HIGH STREET, OXFORD OX1 4BH, UK E-mail:[email protected]
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Abstract

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 $\left( {Imp} \right)^{Imp} \ne Imp$.

Keywords

03E3503E45implicitly constructible universe
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 4 , December 2019 , pp. 1403 - 1421
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

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