A Constructive Interpretation of Ramsey's Theorem via the Product of Selection Functions
Logic
2012-06-04 v2 Logic in Computer Science
Abstract
We use G\"{o}del's Dialectica interpretation to produce a computational version of the well known proof of Ramsey's theorem by Erd\H{o}s and Rado. Our proof makes use of the product of selection functions, which forms an intuitive alternative to Spector's bar recursion when interpreting proofs in analysis. This case study is another instance of the application of proof theoretic techniques in mathematics.
Keywords
Cite
@article{arxiv.1204.5631,
title = {A Constructive Interpretation of Ramsey's Theorem via the Product of Selection Functions},
author = {Paulo Oliva and Thomas Powell},
journal= {arXiv preprint arXiv:1204.5631},
year = {2012}
}