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Results tagged with set-theory
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user 6074
forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
8
votes
Is there a metamathematical $V$?
Let me offer a different perspective, informed by my recent conversion from ZFC to ETCSR, i.e. Lawvere's elementary theory of the category of sets (with replacement). Recall that the two theories are …
- 21.3k
18
votes
Sheaf-theoretic approach to forcing
Thanks for all the enlightening answers! Let me summarize my understanding now. (Please correct me if I'm saying something stupid!)
First, as explained by Mike Shulman in his answer, the answer to Que …
- 21.3k
10
votes
Reflection principle vs universes
A question that came up in the comments was about the motivation for asking the question. Let me try to address this here.
Foremost, it is about learning! As I mentioned in the original question, I ha …
- 21.3k
49
votes
4
answers
7k
views
Sheaf-theoretic approach to forcing
Inspired by the question here, I have been trying to understand the sheaf-theoretic approach to forcing, as in MacLane–Moerdijk's book "Sheaves in geometry and logic", Chapter VI.
A general comment is …
- 21.3k
18
votes
Reflection principle vs universes
OK, I spent much of today trying to figure this out by actually looking in some detail at HTT. It's been quite a ride; I have definitely changed my perspective multiple times in the process. Currently …
- 21.3k
97
votes
10
answers
15k
views
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. The …
- 21.3k
10
votes
Condensed / pyknotic sets in terms of forcing over Boolean-valued models of set theory / mul...
Great question — for some reason this tight relation between extremally disconnected profinite sets and forcing had elapsed me!
I've just been trying to read a bit about it. From what I understand, th …
- 21.3k