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2 results

  • THE UNIQUENESS OF ELEMENTARY EMBEDDINGS

  • Part of
  • GABRIEL GOLDBERG
  • Journal:
    The Journal of Symbolic Logic , First View
    Published online by Cambridge University Press:
    13 December 2024, pp. 1-25
    • Article
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  • Much of the theory of large cardinals beyond a measurable cardinal concerns the structure of elementary embeddings of the universe of sets into inner models. This paper seeks to answer the question of whether the inner model uniquely determines the elementary embedding.

  • THE KETONEN ORDER

  • Part of
  • GABRIEL GOLDBERG
  • Journal:
    The Journal of Symbolic Logic / Volume 85 / Issue 2 / June 2020
    Published online by Cambridge University Press:
    18 June 2020, pp. 585-604
    Print publication:
    June 2020

  • We study a partial order on countably complete ultrafilters introduced by Ketonen [2] as a generalization of the Mitchell order. The following are our main results: the order is wellfounded; its linearity is equivalent to the Ultrapower Axiom, a principle introduced in the author’s dissertation [1]; finally, assuming the Ultrapower Axiom, the Ketonen order coincides with Lipschitz reducibility in the sense of generalized descriptive set theory.