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.
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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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