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  1. What Model Companionship Can Say About the Continuum Problem.Giorgio Venturi & Matteo Viale - 2024 - Review of Symbolic Logic 17 (2):546-585.
    We present recent results on the model companions of set theory, placing them in the context of a current debate in the philosophy of mathematics. We start by describing the dependence of the notion of model companionship on the signature, and then we analyze this dependence in the specific case of set theory. We argue that the most natural model companions of set theory describe (as the signature in which we axiomatize set theory varies) theories of $H_{\kappa ^+}$, as $\kappa (...)
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