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June 2013 Partial impredicativity in reverse mathematics
Henry Towsner
J. Symbolic Logic 78(2): 459-488 (June 2013). DOI: 10.2178/jsl.7802070

Abstract

In reverse mathematics, it is possible to have a curious situationwhere we know that an implication does not reverse, but appear to haveno information on how to weaken the assumption while preserving theconclusion (other than reducing all the way to the tautology ofassuming the conclusion). A main cause of this phenomenon is theproof of a $\Pi^1_2$ sentence from the theory $\mathbf{\Pi^{\textbf{1}}_{\textbf{1}}-CA_{\textbf{0}}}$. Using methodsbased on the functional interpretation, we introduce a family ofweakenings of $\mathbf{\Pi^{\textbf{1}}_{\textbf{1}}-CA_{\textbf{0}}}$ and use them to give new upper bounds for theNash-Williams Theorem of wqo theory and Menger's Theorem for countablegraphs.

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Henry Towsner. "Partial impredicativity in reverse mathematics." J. Symbolic Logic 78 (2) 459 - 488, June 2013. https://doi.org/10.2178/jsl.7802070

Information

Published: June 2013
First available in Project Euclid: 15 May 2013

zbMATH: 1275.03079
MathSciNet: MR3145191
Digital Object Identifier: 10.2178/jsl.7802070

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 2 • June 2013
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