- M. J. Groszek and J. D. Hamkins, “The implicitly constructible universe,” Journal of Symbolic Logic, vol. 84, iss. 4, p. 1403–1421, 2019.

[Bibtex]`@ARTICLE{GroszekHamkins2019:The-implicitly-constructible-universe, AUTHOR = {Groszek, Marcia J. and Hamkins, Joel David}, TITLE = {The implicitly constructible universe}, JOURNAL = {Journal of Symbolic Logic}, FJOURNAL = {The Journal of Symbolic Logic}, VOLUME = {84}, YEAR = {2019}, NUMBER = {4}, PAGES = {1403--1421}, ISSN = {0022-4812}, MRCLASS = {03E35 (03E45)}, MRNUMBER = {4045982}, DOI = {10.1017/jsl.2018.57}, 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 $(\Imp)^{\Imp} \neq \Imp$.