Year: 2011
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Towsner, Henry
Institution: University of Pennsylvania
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2952560565