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  1. The Copernican Multiverse of Sets.Paul K. Gorbow & Graham E. Leigh - 2022 - Review of Symbolic Logic 15 (4):1033-1069.
    We develop an untyped framework for the multiverse of set theory. $\mathsf {ZF}$ is extended with semantically motivated axioms utilizing the new symbols $\mathsf {Uni}(\mathcal {U})$ and $\mathsf {Mod}(\mathcal {U, \sigma })$, expressing that $\mathcal {U}$ is a universe and that $\sigma $ is true in the universe $\mathcal {U}$, respectively. Here $\sigma $ ranges over the augmented language, leading to liar-style phenomena that are analyzed. The framework is both compatible with a broad range of multiverse conceptions and suggests its (...)
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  • Set theoretical analogues of the Barwise-Schlipf theorem.Ali Enayat - 2022 - Annals of Pure and Applied Logic 173 (9):103158.
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