Level theory, part 1: Axiomatizing the bare idea of a cumulative hierarchy of sets

Bulletin of Symbolic Logic 27 (4):436-460 (2021)
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Abstract

The following bare-bones story introduces the idea of a cumulative hierarchy of pure sets: 'Sets are arranged in stages. Every set is found at some stage. At any stage S: for any sets found before S, we find a set whose members are exactly those sets. We find nothing else at S.' Surprisingly, this story already guarantees that the sets are arranged in well-ordered levels, and suffices for quasi-categoricity. I show this by presenting Level Theory, a simplification of set theories due to Scott, Montague, Derrick, and Potter.

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Tim Button
University College London

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