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awarded  Notable Question
Apr
17
answered Does the totality of Ackermann's function prove the consistency of $\Sigma_1$-induction?
Mar
26
asked Does the totality of Ackermann's function prove the consistency of $\Sigma_1$-induction?
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revised Fixed point theorems
Corrected Reference
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Dec
23
comment Peano (Dedekind) categoricity
The paper "Reverse mathematics and Peano categoricity" by Simpson and Yokoama may be related to you question. A preprint is available at personal.psu.edu/t20/papers/rmpc.pdf .
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Sep
26
answered Does the Feferman-Schutte analysis give a precise characterization of Predicative Second-Order Arithmetic?
Jul
12
comment Generalizations of the Tietze extension theorem (and Lusin's theorem)
Tietze's extension theorem also holds for mappings into locally convex spaces, see msp.org/pjm/1951/1-3/pjm-v1-n3-p04-p.pdf .
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comment Can nonstandard analysis be used to prove results in constructive or computable analysis?
I do not know whether this is what you are looking for but Keita Yokoama used non-standard analysis to analyze the strength of the Riemann mapping theorem in terms of reverse mathematics, see math.tohoku.ac.jp/~y-keita/papers/nonst-r-mapping.pdf
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Feb
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comment Partitions of central sets via dynamical systems
Asaf: The sets $S,S′$ are clearly central. But I do not see why this implies that $\{ s_{n′} \mid n′\in S′ \}$ is central. However, this might be what Hillel was thinking about. Maybe there is just an argument missing