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Separating the Fan Theorem and Its Weakenings II

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Logical Foundations of Computer Science (LFCS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10703))

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Abstract

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 re-prove 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.

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Notes

  1. 1.

    If the reader is feeling any frustration at the length and detail of this proof, it might amuse them to know that in an earlier draft, the spot above contained an expletive.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, 33431, USA

    Robert S. Lubarsky

Authors
  1. Robert S. Lubarsky
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Correspondence to Robert S. Lubarsky .

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Editors and Affiliations

  1. City University of New York, New York, New York, USA

    Sergei Artemov

  2. Cornell University, Ithaca, New York, USA

    Anil Nerode

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Lubarsky, R.S. (2018). Separating the Fan Theorem and Its Weakenings II. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2018. Lecture Notes in Computer Science(), vol 10703. Springer, Cham. https://doi.org/10.1007/978-3-319-72056-2_15

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  • DOI: https://doi.org/10.1007/978-3-319-72056-2_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72055-5

  • Online ISBN: 978-3-319-72056-2

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