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Results tagged with reverse-math
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user 10384
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).
14
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Are key theorems finitistically reducible?
There are various problems with finitistic reducibility as Simpson develops it; for a survey, see §5.3 of my Stanford Encyclopedia of Philosophy entry on reverse mathematics. I tend to agree that the …
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5
votes
Equivalences between statements of (seemingly) different order
When we say "with set parameters" I take it that what we really mean is something of the form: the axioms of (e.g.) the $\Sigma^0_1$ induction scheme are the universal closures of all formulas of the …
- 1,094
10
votes
3
answers
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New research on coding in reverse mathematics?
Coding is obviously a fundamental tool in reverse mathematics, and practitioners take care to both demonstrate the correctness of their coding mechanisms and point out their limitations. Harvey Friedm …
- 4,359
5
votes
1
answer
231
views
Attribution of an equivalence of the existence of omega-models of RCA0
There are many well-known equivalences in reverse mathematics between statements of the form "Every set is contained a countable coded $\omega$-model of $T$" and $S$, where $S, T$ are subsystems of se …
CommunityBot
- 1
7
votes
0
answers
511
views
Fragments of Morse—Kelley set theory
Morse—Kelley set theory (hereafter MK) is the impredicative counterpart of von Neumann—Bernays—Gödel set theory (NBG), where formulas containing class quantifiers are permitted in the comprehension sc …
- 1,094