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    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 18th 2018

    Since I gathered them for my recent talk, I may as well provide a list here of work in this area. I need to add names, etc.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 18th 2018

    I was wondering, famously because the internal language of a topos is not classical it is possible to add classically inconsistent axioms, such as the Kock-Lawvere axiom. Can something similar occur with HoTT?

    At this new axioms section it points out that we may add things like Whitehead’s axiom, but this goes in the direction of making things more classical. How about something which relies on the constructive aspect of HoTT?

    Hmm, or might modalities play this role?

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 19th 2018

    Fixed incorrect link to Felix Wellen’s abstract for HoTTUF18

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeAug 19th 2018

    Yes, “Axiom R” in my realcohesion paper is a nonclassical axiom, inconsistent with full LEM. It doesn’t require higher homotopy, but it becomes much more powerful in the presence of it.

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 8th 2019

    Added another

    • Kristina Sojakova, The equivalence of the torus and the product of two circles in homotopy type theory, (arXiv:1510.03918)

    diff, v14, current

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