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    • CommentRowNumber1.
    • CommentAuthorBrian Pinsky
    • CommentTimeJan 3rd 2021

    These two related principals are not the only axioms with this name. A more set-theoretic “axiom of multiple choice” also exists (which, as far as I can tell, is unrelated to these axioms). I added the set theoretic axiom and gave some references where it is used this way.

    diff, v15, current

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJan 3rd 2021

    Again, I think it’s worth considering creating a separate page for this other notion you’re referring to. See my earlier comment in the other thread.

  1. removing query box from article

    +–{: .query} Mike Shulman: Are the first two the same? If not, why are they given the same name?

    Peter LeFanu Lumsdaine: Yes, they are equivalent. For any XX, given a collection family {D c} cC\{D_c\}_{c \in C} including XX, then the family {D c} (cC,f:D cX)\{D_c\}_{(c \in C, f : D_c \twoheadrightarrow X)}” is an inhabited collection family equipped with surjections to XX. Conversely, given an inhabited collection family equipped with surjections to XX, throwing XX into the family gives a collection family including XX. =–


    diff, v19, current