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Results tagged with set-theory
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user 3154
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.
5
votes
When is something too big to be a set?
I find the terminology of "too big" to be misleading. I think it comes about from thinking that the strength of a set theory comes from the generosity of its comprehension axioms, that stronger set t …
- 2,283
4
votes
Can we prove set theory is consistent?
I think you are describing a process that is a fairly accurate description of how set theorists typically think about issues of consistency, where Set1 is the informal account of the cumulative hierar …
- 2,283
3
votes
The Importance of ZF
This answer is essentially a Joel's version by another route.
ZF(C), possibly with appropriate large cardinal axioms, is one of the three most important formal axiomatisations in the foundations of m …
- 2,283
2
votes
Models of ZFC Set Theory - Getting Started
From comment: how do we get from "the abstract" to "the concrete"?
In my partly informed opinion, not by formal model theory! The ability of set theory to describe its own models is one of the pilla …
- 2,283
5
votes
Uses of bisimulation outside of computer science.
It's used in modal logic, where it was invented, and is used to define relations between models and constructions of new models from old models, which are used to show that different classes of model …
- 2,283