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2 results

  • SEPARATING THE FAN THEOREM AND ITS WEAKENINGS II

  • ROBERT S. LUBARSKY
  • Journal:
    The Journal of Symbolic Logic / Volume 84 / Issue 4 / December 2019
    Published online by Cambridge University Press:
    25 July 2019, pp. 1484-1509
    Print publication:
    December 2019

  • Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Earlier work showed all of these implications to be strict. Here we reprove one of the strictness results, using very different arguments. The technique used is a mixture of realizability, forcing in the guise of Heyting-valued models, and Kripke models.

  • SEPARATING THE FAN THEOREM AND ITS WEAKENINGS

  • ROBERT S. LUBARSKY, HANNES DIENER
  • Journal:
    The Journal of Symbolic Logic / Volume 79 / Issue 3 / September 2014
    Published online by Cambridge University Press:
    18 August 2014, pp. 792-813
    Print publication:
    September 2014

  • Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which separates all of the as yet identified fan theorems.