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arXiv · 1106.6063

Partial Impredicativity in Reverse Mathematics

Henry Towsner
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Abstract

In reverse mathematics, is is possible to have a curious situation where we know that an implication does not reverse, but appear to have no information on on how to weaken the assumption while preserving the conclusion. A main cause of this phenomenon is the proof of a $Π^1_2$ sentence from the theory {\Pioo}. Using methods based on the functional interpretation, we introduce a family of weakenings of {\Pioo} and use them to give new upper bounds for the Nash-Williams Theorem of wqo theory and Menger's Theorem for countable graphs.

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Henry Towsner. 2012-11-30. Partial Impredicativity in Reverse Mathematics. https://arxiv.org/abs/1106.6063

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