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Results tagged with set-theory
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user 31233
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.
9
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0
answers
374
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Reflection principle for intuitionistic Zermelo–Fraenkel?
The well-known reflection principle for classical Zermelo–Fraenkel states:
For any formula $\varphi(x_1,\ldots,x_n)$ of the language of ZFC with free variables $x_1,\ldots,x_n$, ZFC proves
$$ \f …
- 3,312
7
votes
2
answers
1k
views
Explaining the consistency of PRA and ZF from predicative foundations
Recently I got interested in predicative foundations, mostly because of Laura Crosilla's work and because Agda employs a predicative type theory.
From the point of view of a predicative foundation to …
- 3,312
3
votes
Explaining the consistency of PRA and ZF from predicative foundations
Last week, I learned from Ulrik Buchholtz that there are proof-theoretic reductions from certain impredicative systems to certain predicative ones. While these fall short of predicatively explaining t …
- 3,312