Approximating Impredicativity in Reverse Mathematics

Details Approximating Impredicativity in Reverse Mathematics Approximating Impredicativity in Reverse Mathematics

2011-06-29

arxiv.org/abs/1106.6063v1

Mathematics

Logic

Scientific paper

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 $\Pi^1_2$ 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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