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Results tagged with set-theory
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user 11640
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.
2
votes
0
answers
146
views
Are partial elements necessary in boolean-valued models?
It seems to me that there is a difference in the treatment of "partial" elements in boolean-valued models in set theory vs topos theory: in set theory, one usually only considers "global" elements of …
- 15.9k
6
votes
2
answers
451
views
When are all greater cardinals sharply greater?
Makkai and Paré introduced the following binary relation on regular cardinals: given $\kappa$ and $\lambda$, $\kappa \vartriangleleft \lambda$ (read, $\kappa$ is sharply less than $\lambda$) when $\k …
- 15.9k
18
votes
Accepted
Category and the axiom of choice
Here's a somewhat trivial one, but it is one that category theorists use all the time:
Let us say that a functor $F : \mathcal{C} \to \mathcal{D}$ is a weak equivalence if it is fully faithful and …
- 15.9k
22
votes
Sheaf-theoretic approach to forcing
I think the language of classifying toposes is helpful in understanding this view of forcing.
Let $P$ be a poset.
The set theorists have the intuition that forcing over $P$ adjoins a generic filter of …
- 15.9k
7
votes
1
answer
204
views
Finitistic interpretation of Nelson's internal set theory
What does “standard” in internal set theory really mean?
Is it secretly a way of reconciling conventional mathematics with (ultra)finitism?
Until recently I thought “standard” was just a way of talkin …
- 15.9k