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Results tagged with reverse-math
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user 12978
The general enterprise of calibrating the strength of classical mathematical theorems in terms of the axioms, typically of set existence, needed to prove them; originated in its modern form in the 1970s by H. Friedman and S. G. Simpson (see R.A. Shore, "Reverse Mathematics: The Playground of Logic", 2010).
6
votes
Accepted
Formal definition of arithmetic transfinite recursion
To repeat Emil and Andreas's comments, it can be found in Stephen G. Simpson, "Systems of Second-Order Arithmetic", the first chapter of which is available here:
http://www.personal.psu.edu/t20/sosoa …
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1
vote
Proving moduli of uniform continuity in RCA_0
On a space like $\mathbb{R}^n$, $[0,1]^n$, or $\mathbb{C}$, every uniformly continuous function that "arises in practice" (more on this in a bit) has a computable modulus of continuity.
To find examp …
- 6,287
7
votes
Accepted
reverse mathematics strength of "Lipschitz functions are somewhere differentiable"
(Update: I made my answer clearer and also fixed the references and added more.)
Your theorem should be true in every $\omega$-model of $\mathsf{RCA}_0$ as follows. The following paper
Brattka, Mil …
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4
votes
Understanding the nature and structure of proofs; Reverse Mathematics and Proof Theory. Prer...
As for your question on prerequisites, the more logic you know the better. Of course the basic concepts---proofs, models, Peano arithmetic, incompleteness, compactness, nonstandard models, primitive …
8
votes
7
answers
648
views
Strength of Bishop style constructive mathematics vs $\mathsf{RCA}_0$
This question came out of this other MO question of mine. My question is
Is there a formal comparison between $\mathsf{RCA}_0$ and $\mathsf{BISH}$ (Bishop style constructive mathematics as used in c …
- 6,287
23
votes
2
answers
2k
views
Prospects for reverse mathematics in Homotopy Type Theory
Reverse mathematics, as I mean here, is the study of which theorems/axioms can be used to prove other theorems/axioms over a weak base theory. Examples include
Subsystems of Second Order Arithmetic …
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