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LEVEL THEORY, PART 3: A BOOLEAN ALGEBRA OF SETS ARRANGED IN WELL-ORDERED LEVELS

Part of: Philosophical aspects of logic and foundations Set theory

Published online by Cambridge University Press:  28 April 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

On a very natural conception of sets, every set has an absolute complement. The ordinary cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining classical logic. Indeed, we can develop a boolean algebra of sets arranged in well-ordered levels. I show this by presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly implement Conway’s games and surreal numbers; and a natural extension of BLT is definitionally equivalent with ZF.

Keywords

set theorylevel theoryuniversal set

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 28 , Issue 1 , March 2022 , pp. 1 - 26
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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