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  1. starting article on the differences between set theory and dependent type theory


    v1, current

  2. renaming in parallel with material versus structural set theories


    v1, current

  3. added section on how functions differ between set theory and type theory.


    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 21st 2023

    I have added more hyperlinks to the relevant technical terms such as “categorical set theory” or “family of elements”.

    (I may seem pedantic, but let’s think about this: Since your paragraph here necessarily addresses readers who do not know or do not agree on something as fundamental as the notion of “functions” in set theory, is it reasonable to assume that such readers know or agree on what “categorical set theory” of “families of elements” are? I think the answer is clearly: no. In any case, let’s consistently enclose technical terms in double square brackets to hyperlink them. It’s meant to be quick and easy (“wiki” means “quick”!) and is among the main points of writing into a hypertext-wiki in the first place: to have every claim provide links to its necessary background notions.)

    By the way, the last sentence currently is hard to parse:

    The corresponding primitive notion is the concept of family of elements x:Af(x):Bx \colon A \vdash f(x) \colon B, of which there is no corresponding notion of equality of a family of elements.

    Probably the duplication is accidental and you mean to say:

    The corresponding primitive notion is the concept of family of elements x:Af(x):Bx \colon A \vdash f(x) \colon B, of which there is no corresponding notion of equality.

    But then I am wondering: Is this really true?

    diff, v3, current