2023/11/12 by Martin Balko, David Chodounský, Balko, Martin +11
Computer Science · Mathematics · #05C05 #05C55 #05C65 #05D10 #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #Discrete Mathematics (cs.DM) #F.4.1 #FOS: Computer and information sciences #FOS: Mathematics #G.2.2 #Limits and Structures in Graph Theory #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2311.06872
openalex publication_date 2023/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We prove a general Ramsey theorem for trees with a successor operation. This theorem is a common generalization of the Carlson-Simpson Theorem and the Milliken Tree Theorem for regularly branching trees. Our theorem has a number of applications both in finite and infinite combinatorics. For example, we give a short proof of the unrestricted Nešetřil-Rödl theorem, and we recover the Graham-Rothschild theorem. Our original motivation came from the study of big Ramsey degrees - various trees used in the study can be viewed as trees with a successor operation. To illustrate this, we give a non-forcing proof of a theorem of Zucker on big Ramsey degrees.