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Anonymous

• CommentRowNumber2.
• CommentAuthorGuest
• CommentTimeOct 5th 2022

Tarski universes are supposed to refer to the entire structure consisting of a type $U$ and the type family $El$, not just the type $U$. 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

Anonymous

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

Anonymous

4. added section on hierarchies of Tarski universes

Anonymous

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.

Anonymous

Anonymous

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

Anonymous

• 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.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeJan 22nd 2023

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