Questions tagged [reverse-math]

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).

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).

166 questions
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Soundness Theorem in reverse mathematics

STPL := soundness theorem for predicate logic (see this) When trying to figure out the strength of the STPL in reverse mathematics, I managed to convince myself of the following: a) ACA0 has a (provably) $\Delta_1^1$ pair of formulas, which it…
user5810
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Circular reasoning in proof of bounded comprehension

Theorems II.3.7 and II.3.9 in Simpson's Subsystems of Second-Order Arithmetic appear to be circular. Specifically, theorem II.3.7 seems to make implicit use of theorem II.3.9. [Theorem II.3.9 is the principle of bounded $\Sigma_1$ comprehension.…
A.C.
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Two questions regarding the reverse mathematics of Siegel's lemma

In a short proof of the Roth theorem regarding the rational approximation of algebraic reals I found online (which made use of Siegel's Lemma), it was stated that "Siegel's lemma is a corollary of the 'pigeonhole principle'". In their paper, "Where…