2019/01/14 by Eugenio Colla, Colla, Eugenio, Domenico Zambella +1
Computer Science · Mathematics · #03C98 #03H99 (Secondary) #05D10 (Primary) #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO)
paper · doi:10.48550/arxiv.1901.04363
openalex publication_date 2019/01/14 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
We use the model theoretic notion of coheir to give short proofs of old and new theorems in Ramsey Theory. As an illustration we start from Ramsey's theorem itself. Then we prove Hindman's theorem and the Hales-Jewett theorem. Finally, we prove two Ramsey theoretic principles that have among their consequences partition theorems of Carlson and of Gowers.