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nLab > Latest Changes: class theory

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  1. starting article on class theory

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 19th 2022
    • (edited Nov 19th 2022)

    Thanks for these substantial additions.

    Just some trivia on formatting and style:

    • To set the scene for the reader, I have prefixed the opening sentence by the words “In the foundations of mathematics…” (also included the respective floating context menu).

    • Where “material and structural” are first mentioned, I have hyperlinked these words.

    • The two long sentences that followed I have taken the liberty of breaking up for readability: I have turned “… and classes are…” into “… Here, classes are…”

    • Generally, I have hyperlinked more of the technical terms, such as theory, formulae, size issue, model, higher structure etc.

    • Speaking of higher structures: it remains unclear to me what the following paragraph currently in the entry is meant to achieve:

    While class theories address the issue of size in mathematics, they violate the principle of equivalence for higher structures like groupoids, because, like sets in set theory, every class in class theory has propositional equality, including groupoids defined in class theory.

    It seems to me the two issues here are orthogonal to each other. Or maybe you are thinking specifically of large groupoids, like the groupoid of all sets? If so, that would be good to clarify.

    diff, v3, current

  3. Adding reference

    • Henrik Forssell, Categorical Models of Intuitionistic Theories of Sets and Classes. Master’s thesis, Carnegie Mellon University, 2004. (PDF)

    Anonymous

    diff, v5, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2022

    Let me know if you have thoughts regarding the last point in #2. Otherwise I feel like deleting the paragraph in question there, since in its current form it does not seem to make sense.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 22nd 2022

    In lack of a reply to my question in #2, I am removing this paragraph from the entry:

    While class theories address the issue of size in mathematics, they violate the principle of equivalence for higher structures like groupoids, because, like sets in set theory, every class in class theory has propositional equality, including groupoids defined in class theory.

    I don’t see how this makes sense as formulated. If anyone sees what was meant and can expand, please do and we put the paragraph back in.

    diff, v7, current

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