English

The Implicitly Constructible Universe

Logic 2020-02-19 v1

Abstract

We answer several questions posed by Hamkins and Leahy concerning the implicitly constructible universe, Imp. Specifically, we show that it is relatively consistent with ZFC that Imp satisfies the negation of CH, that Imp is not HOD, and that Imp satisfies V \neq Imp, or in other words, that (Imp)ImpImp(Imp)^{Imp}\neq Imp.

Cite

@article{arxiv.1702.07947,
  title  = {The Implicitly Constructible Universe},
  author = {Marcia J. Groszek and Joel David Hamkins},
  journal= {arXiv preprint arXiv:1702.07947},
  year   = {2020}
}

Comments

20 pages. Commentary concerning this article can be made on the second author's blog at http://jdh.hamkins.org/the-implicitly-constructible-universe

R2 v1 2026-06-22T18:28:29.983Z