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Level Theory, Part 1: Axiomatizing The Bare Idea Of A Cumulative Hierarchy Of Sets

Button, T; (2021) Level Theory, Part 1: Axiomatizing The Bare Idea Of A Cumulative Hierarchy Of Sets. Bulletin of Symbolic Logic , 27 (4) pp. 436-460. 10.1017/bsl.2021.13. Green open access

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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.

Type: Article
Title: Level Theory, Part 1: Axiomatizing The Bare Idea Of A Cumulative Hierarchy Of Sets
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/bsl.2021.13
Publisher version: http://doi.org/10.1017/bsl.2021.13
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Dept of Philosophy
URI: https://discovery.ucl.ac.uk/id/eprint/10126813
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