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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: marcia.groszek@dartmouth.edu
JOEL DAVID HAMKINS
Affiliation:
FACULTY OF PHILOSOPHY UNIVERSITY COLLEGE, OXFORD HIGH STREET, OXFORD OX1 4BH, UK E-mail:joeldavid.hamkins@philosophy.ox.ac.uk
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Abstract

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

Keywords

03E3503E45implicitly constructible universe

Information

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 

References

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