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Level theory. II: Axiomatizing the bare idea of a potential hierarchy. (English) Zbl 07482182

Summary: Potentialists think that the concept of set is importantly modal. Using tensed language as a heuristic, the following bare-bones story introduces the idea of a potential hierarchy of sets: ‘Always: for any sets that existed, there is a set whose members are exactly those sets; there are no other sets’. Surprisingly, this story already guarantees well-foundedness and persistence. Moreover, if we assume that time is linear, the ensuing modal set theory is almost definitionally equivalent with non-modal set theories; specifically, with Level Theory, as developed in Part 1 [the author, ibid. 27, No. 4, 436–460 (2021; Zbl 07482181)].

MSC:

03E30 Axiomatics of classical set theory and its fragments
03E70 Nonclassical and second-order set theories

Citations:

Zbl 07482181
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References:

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