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  1. Truth is Simple.Leon Horsten & Graham E. Leigh - 2017 - Mind 126 (501):195-232.
    Even though disquotationalism is not correct as it is usually formulated, a deep insight lies behind it. Specifically, it can be argued that, modulo implicit commitment to reflection principles, all there is to the notion of truth is given by a simple, natural collection of truth-biconditionals.
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    Proof Systems for Two-Way Modal Mu-Calculus.Bahareh Afshari, Sebastian Enqvist, Graham E. Leigh, Johannes Marti & Yde Venema - forthcoming - Journal of Symbolic Logic:1-50.
    We present sound and complete sequent calculi for the modal mu-calculus with converse modalities, aka two-way modal mu-calculus. Notably, we introduce a cyclic proof system wherein proofs can be represented as finite trees with back-edges, i.e., finite graphs. The sequent calculi incorporate ordinal annotations and structural rules for managing them. Soundness is proved with relative ease as is the case for the modal mu-calculus with explicit ordinals. The main ingredients in the proof of completeness are isolating a class of non-wellfounded (...)
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    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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