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Publication Detail
LEVEL THEORY, PART 3: A BOOLEAN ALGEBRA OF SETS ARRANGED IN WELL-ORDERED LEVELS
  • Publication Type:
    Journal article
  • Authors:
    BUTTON TIM
  • Publisher:
    Cambridge University Press (CUP)
  • Publication date:
    03/2022
  • Pagination:
    1, 26
  • Journal:
    The Bulletin of Symbolic Logic
  • Volume:
    28
  • Issue:
    1
  • Status:
    Published
  • Print ISSN:
    1079-8986
  • Language:
    en
Abstract
AbstractOn 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.
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