Linked Questions
11 questions linked to/from What interesting/nontrivial results in Algebraic geometry require the existence of universes?
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Reflection principle vs universes
In category-theoretic discussions, there is often the temptation to look at the category of all abelian groups, or of all categories, etc., which quickly leads to the usual set-theoretic problems. ...
32
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4
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Who needs Replacement anyway?
The set theory ETCS famously comes without the Replacement axiom schema (or an equivalent) that is part of ZFC. One (to me, not apparently useful) set that one cannot build in ETCS is $\coprod_{n\in \...
38
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Do Grothendieck universes matter for an algebraic geometer?
I recently learned that some parts of SGA require axioms beyond ZFC. I am just a simple algebraic geometer so I am trying to understand how can this fact impact my life (you may have engaged in a ...
14
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1
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"Largish" cardinals
In what follows, $\mathsf{ZCKP}$ refers to the subset of $\mathsf{ZFC}$ consisting of the axioms of Zermelo set theory with choice and foundation ($\mathsf{ZC}$) plus those of Kripke-Platek set theory ...
11
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What is the use of Grothendieck universes in category theory?
First of all, I have to mention that I'm truly sorry if this question would seem inappropriate for this site for some people. Still, I think it is better to ask here rather on math.stackexchange.
I ...
8
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1
answer
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Abandoned LCAs on Cantor's Attic : Grand Reflection cardinals, universe cardinals, weak universe cardinals
Cantor's Attic is a really great website for the various descriptions of large finite numbers, large countable ordinals, and large cardinal axioms.
However, after looking through the archives of the ...
28
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Is Feferman's unlimited category theory dead?
In 2013 Solomon Feferman in Foundations of unlimited category theory: what remains to be done (The Review of Symbolic Logic, 6 (2013) pp 6-15, link) laid out three desirable axioms for "...
3
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1
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Very weak notions of Universes in ZFC
Let us work in ZFC set theory.
1: We name "Very very weak universe (VVWU)" a set u such that if a and b are two member sets of u, then every function between a and b is also a member set of u; The ...
7
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1
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Can we have more malleable proper classes without sacrificing conservativity?
NBG is a conservative extension of ZFC that includes a concept of "proper class." Now I like the conservativity, since it means anytime I want to prove something in ZFC, I am free to work in NBG. ...
6
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2
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Size issues in localization $\mathcal{C}[\mathcal{W}^{-1}]$ category
When one starts with a locally small category $\mathcal{C}$ and wants to localize it at an appropriate choosen collection of morphisms $\mathcal{W}$, then in general one faces some size issues in the ...
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On the foundations for large categories
There are some basic discussions on the motivations of large categories and small categories: On the large cardinals foundations of categories, Large cardinal axioms and Grothendieck universes, Small ...