Partial Impredicativity in Reverse Mathematics
Logic
2012-12-03 v2
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 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.
Cite
@article{arxiv.1106.6063,
title = {Partial Impredicativity in Reverse Mathematics},
author = {Henry Towsner},
journal= {arXiv preprint arXiv:1106.6063},
year = {2012}
}