2010/08/26 by Peter Cholak, Cholak, Peter, David Galvin +3
Computer Science · Mathematics · Psychology · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Philosophy and Theoretical Science #math.LO
paper · pdf · doi:10.48550/arxiv.1008.4548
openalex publication_date 2010/08/26 · arxiv created 2011/01/03 · arxiv updated 2011/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper falls within the general program of investigating the proof theoretic strength (in terms of reverse mathematics) of combinatorial principals which follow from versions of Ramsey's theorem. We examine two statements in graph theory and one statement in lattice theory proved by Galvin, Rival and Sands \citeGRS:82 using Ramsey's theorem for 4-tuples. Our main results are that the statements concerning graph theory are equivalent to Ramsey's theorem for 4-tuples over \RCA while the statement concerning lattices is provable in \RCA. Revised 12/2010. To appear in Archive for Mathematical Logic