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Publication Detail
LEVEL THEORY, PART 1: AXIOMATIZING THE BARE IDEA OF A CUMULATIVE HIERARCHY OF SETS
  • Publication Type:
    Journal article
  • Authors:
    BUTTON TIM
  • Publisher:
    Cambridge University Press (CUP)
  • Publication date:
    12/2021
  • Pagination:
    436, 460
  • Journal:
    The Bulletin of Symbolic Logic
  • Volume:
    27
  • Issue:
    4
  • Status:
    Published
  • Print ISSN:
    1079-8986
  • Language:
    en
Abstract
AbstractThe 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.
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