# Tagged Questions

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", ...

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### What is the reverse mathematical strength of the fundamental theorem of algebra?

Reverse mathematics (RM) is that area that tries to pin down exactly which axioms are necessary to prove theorems, given some weak base theory. Harvey Friedman has pointed out several times (on the ...
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### Z_2 versus second-order PA

These days, Peano Arithmetic ($PA$) refers to the first-order version of the axioms, where induction is only over formulas referring to natural number variables. Peano's original version of the ...
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### Applicability of Deduction theorem to Primitive recursive arithmetic [closed]

Hello. I already asked the question here. The main point is that I tried to prove in Primitive recursive arithmetic (PRA) the totality of the Ackerman function, and I found, that the single thing ...
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### How do you restrict the induction axiom in second (or higher) order logic?

Dear all, I am interested in reverse mathematics. The theory is that most of mathematics can be expressed and proven in ACA0, that is second order logic, with the induction axiom restricted. ...
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### Non-Computational classical subterms

Assume we have a proof term of the form $(a^{A\rightarrow^c B\rightarrow^{nc} C}b^Ac^B)^C$, where $c$ is classical (that is, contains free instances of duplex negatio affirmat). The extracted term ...
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### reverse mathematics strength of “Lipschitz functions are somewhere differentiable”

What is the reverse mathematics strength of "For all Lipschitz functions $\; f : \mathbb{R} \to \mathbb{R} \;$, $\;$ there exists a real number $x$ such that $f$ is differentiable at $x$." ? ...
To be more precise, a countable collection of sets $(S_n)_{n \in \mathbb{N}}$ is encoded as the row of some given set $S$, i.e. $S_n = S^{[n]}$. Futhermore, for any function from \$\mathbb{N} ...