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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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  • End extending models of set theory via power admissible covers.Zachiri McKenzie & Ali Enayat - 2022 - Annals of Pure and Applied Logic 173 (8):103132.
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  • Condensable models of set theory.Ali Enayat - 2022 - Archive for Mathematical Logic 61 (3):299-315.
    A model \ of ZF is said to be condensable if \\prec _{\mathbb {L}_{{\mathcal {M}}}} {\mathcal {M}}\) for some “ordinal” \, where \:=,\in )^{{\mathcal {M}}}\) and \ is the set of formulae of the infinitary logic \ that appear in the well-founded part of \. The work of Barwise and Schlipf in the 1970s revealed the fact that every countable recursively saturated model of ZF is cofinally condensable \prec _{\mathbb {L}_{{\mathcal {M}}}}{\mathcal {M}}\) for an unbounded collection of \). Moreover, it (...)
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