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What are the proof-theoretic strengths of Ramsey's theorems?

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#logic #ramsey-theory #reverse-math #ordinal-analysis
107
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What is the proof theoretic ordinal of $\mathsf{B\Sigma}_{2}^{0}$?

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#logic #second-order-logic #reverse-math #ordinal-analysis
73
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Why does $\mathsf{WKL}_{0}$ not prove Ramsey's Theorem for singletons?

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#logic #ramsey-theory #reverse-math
147
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Real numbers cannot be constructed?

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#computability #axioms #constructive-mathematics #reverse-math
135
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Reverse mathematics and determinacy theorems

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#set-theory #game-theory #borel-sets #reverse-math
69
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Understanding the system $\textbf{ACA}_0'$ and and exercise $6.26$ of Hirschfeldt

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#computability #peano-axioms #reverse-math
51
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represent polynomials as linear combinations of a kind of radial basis functions

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#measure-theory #polynomials #approximation-theory #reverse-math #radial-basis-functions
67
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Is the range of a total $\Pi^1_1$ function $\Delta^1_1$?

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#logic #computability #second-order-logic #reverse-math
107
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$t(x) - t(x/2) + t(x/3) - t(x/4) + ... = 0$ implies $t(x) + t(x/2)+t(x/3)+t(x/4) = C x$?

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#functional-equations #reverse-math #alternating-expression
61
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Reverse mathematics of characterization of compact spaces

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#general-topology #logic #compactness #computability #reverse-math
61
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Is $\mathsf{I}\Sigma_n^0$ is the first-order part of $\Sigma_n^0$-$\mathsf{CA}_0$?

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#logic #induction #reverse-math
572
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Is the set of all algorithms computable?

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#logic #algorithms #computability #reverse-math
79
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What is the significance of the difference between I$\Sigma_3$, I$\Sigma_{30}$ and I$\Sigma_{3000000}$ and $PA$?

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#logic #soft-question #model-theory #reverse-math
37
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Simpson's proof that $\textbf{WKL}_0$ proves existence of recursively saturated models.

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#logic #propositional-calculus #reverse-math
32
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Simpson's proof of the Gandy Kreisel Tait theorem in $\textbf{ATR}_0$

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#logic #descriptive-set-theory #reverse-math

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