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1 results

  • Slim models of Zermelo set theory

  • A. R. D. Mathias
  • Journal:
    The Journal of Symbolic Logic / Volume 66 / Issue 2 / June 2001
    Published online by Cambridge University Press:
    12 March 2014, pp. 487-496
    Print publication:
    June 2001

  • Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula Φ(λ, a) such that for any sequence ⟨Aλ ∣ λ a limit ordinal⟩ where for each λ. Aλ ⊆ λ2, there is a supertransitive inner model of Zermelo containing all ordinals in which for every λAλ = {a ∣ Φ(λ, a)}.