- M. J.~Groszek and J. D. Hamkins, “The implicitly constructible universe,” ArXiv e-prints, 2017. (under review)
@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 = {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 $(\Imp)^{\Imp} \neq \Imp$.