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LEVEL THEORY, PART 1: AXIOMATIZING THE BARE IDEA OF A CUMULATIVE HIERARCHY OF SETS

Part of: Set theory Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  06 May 2021

TIM BUTTON
TIM BUTTON*
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY COLLEGE LONDON GOWER STREET, LONDON, WC1E 6BT, UK E-mail: tim.button@ucl.ac.uk URL: http://www.nottub.com
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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.

Keywords

set theorylevel theoryrankordinal

MSC classification

Primary: 03A05: Philosophical and critical
Secondary: 03E30: Axiomatics of classical set theory and its fragments
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 27 , Issue 4 , December 2021 , pp. 436 - 460
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Copyright
The Author(s), 2021. Published by Cambridge University Press on behalf of Association for Symbolic Logic

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