• M. J.~Groszek and J. D. Hamkins, “The implicitly constructible universe,” ArXiv e-prints, 2017. (manuscript under review)  
  Citation arχiv

  @ARTICLE{GroszekHamkins:The-implicitly-constructible-universe,
  author = {Marcia J.~Groszek and Joel David Hamkins},
  title = {The implicitly constructible universe},
  journal = {ArXiv e-prints},
  year = 2017,
  month = feb,
  volume = {},
  number = {},
  pages = {},
  month = {},
  note = {manuscript under review},
  abstract = {},
  keywords = {under-review},
  source = {},
  doi = {},
  eprint = {1702.07947},
  archivePrefix = {arXiv},
  primaryClass = {math.LO},
  url = {http://jdh.hamkins.org/the-implicitly-constructible-universe},
  }

Abstract. We answer several questions posed by Hamkins and Leahy concerning the implicitly constructible universe $\newcommand\Imp{\text{Imp}}\Imp$, which they introduced in their paper, Algebraicity and implicit definability in set theory. Specifically, we show that it is relatively consistent with ZFC that $\Imp \models \neg \text{CH}$, that $\Imp \neq \text{HOD}$, and that $\Imp \models V \neq \Imp$, or in other words, that $(\Imp)^{\Imp} \neq \Imp$.