2022
DOI: 10.1002/malq.202000026
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Choiceless large cardinals and set‐theoretic potentialism

Abstract: We define a potentialist system of ZF-structures, i.e., a collection of possible worlds in the language of ZF connected by a binary accessibility relation, achieving a potentialist account of the full background set-theoretic universe V . The definition involves Berkeley cardinals, the strongest known large cardinal axioms, inconsistent with the Axiom of Choice. In fact, as background theory we assume just ZF. It turns out that the propositional modal assertions which are valid at every world of our system are… Show more

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