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Dec
3
awarded  Curious
Dec
2
accepted Is below every cohesive set a 1-generic?
Dec
2
asked Is below every cohesive set a 1-generic?
May
17
awarded  Self-Learner
May
17
awarded  Yearling
Apr
28
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?
Feb
16
awarded  Necromancer
Jan
23
awarded  Excavator
Jan
23
revised Fixed point theorems
Corrected Reference
Jan
21
awarded  Civic Duty
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 .
Oct
1
awarded  Caucus
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 .
Jun
25
awarded  Informed
Jun
25
awarded  Revival
Jun
25
awarded  Yearling
Apr
26
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