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Results tagged with foundations
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user 2004
Mathematical logic, Set theory, Peano arithmetic, Model theory, Proof theory, Recursion theory, Computability theory, Univalent foundations, Reverse mathematics, Frege foundation of arithmetic, Goedel's incompleteness and Mathematics, Structural set theory, Category theory, Type theory.
4
votes
Accepted
What restriction(s) of Goedel's primitive recursive functionals is (are) necessary and suffi...
Sorry for taking a bit longer to answer: Everything I say here is from Jeremy Avigad and Sol Feferman's article in the Handbook of Proof Theory, Gödel’s functional (“Dialectica”) interpretation: http: …
- 1,467
5
votes
Can the Burgess-Hazen analysis of Predicative Arithmetic be extended to Transfinite Types?
I'm not aware of anyone doing the setup exactly as you describe, although it is very likely that it has been done, because it is very similar to Kreisel's proposed method of analyzing finitism in Ordi …
- 1,467
5
votes
Has the Ramified Theory of Types been applied to NBG?
You may be interested in Feferman's Unfolding Program, which gives a predicative closure to any schematic theory such as PA or ZFC. The unfolding of PA has the same strength as ATR$_0$, and Feferman c …
- 1,467