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  1. Page created, but author did not leave any comments.


    v1, current

    • CommentRowNumber2.
    • CommentAuthorGuest
    • CommentTimeOct 5th 2022

    Tarski universes are supposed to refer to the entire structure consisting of a type UU and the type family ElEl, not just the type UU. So the corresponding name should be “univalent type with a type family” rather than “univalent index type of a type family”.

  2. Renamed due to parallels with other univalent objects like univalent category and univalent universe


    v1, current

  3. expanded article significantly and renamed article to Tarski universe; the whole reason why one would want such an object is to build up various notions of Tarski universes in type theory, which may or may not be strictly or weakly closed under various type formers in the type theory


    diff, v6, current

  4. added section on hierarchies of Tarski universes


    diff, v7, current

  5. added a definition of Tarski universe which does not involve a type family. This parallels the case in set theory where a family of sets is the fibers of a function rather than being a primitive concept.


    diff, v25, current

  6. added paragraph about definitional univalence for Tarski universes


    diff, v26, current

  7. added a section regarding closure of universes under all propositions.


    diff, v30, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJan 21st 2023

    added what I guess is the original reference:

    and expanded out this bibitem:

    The entry used to point the reader to section 2.1.6 in there. But at least the above pdf version has no such section, instead the section titled “Universes” is 2.3.5. So I changed this, but let me know if I am missing something.

    diff, v31, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJan 22nd 2023

    added pointer to:

    diff, v32, current