Button, Tim;
(2024)
Wand/set theories: a realization of Conway's Mathematicians' Liberation Movement, with an application to Church's set theory with a universal set.
The Journal of Symbolic Logic
10.1017/jsl.2024.21.
(In press).
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Abstract
Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands). By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive way of fleshing out this idea is synonymous with a ZF-like theory. This Theorem has rich applications; it realizes John Conway's (1976) Mathematicians' Liberation Movement; and it connects with a lovely idea due to Alonzo Church (1974).
| Type: | Article |
|---|---|
| Title: | Wand/set theories: a realization of Conway's Mathematicians' Liberation Movement, with an application to Church's set theory with a universal set |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1017/jsl.2024.21 |
| Publisher version: | https://doi.org/10.1017/jsl.2024.21 |
| Language: | English |
| Additional information: | Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Association for Symbolic Logic. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | set theory, level theory, Church’s set theory, universal set, John Conway |
| 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/10190343 |
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