2014/08/11 by Wei Wang
Computer Science · Mathematics · #Advanced Topology and Set Theory #Benford’s Law and Fraud Detection #Combinatorial explosion #Combinatorial principles #Combinatorics #Computability, Logic, AI Algorithms #Computer science #Discrete mathematics #Mathematics #Ramsey theory #Ramsey's theorem #Set (abstract data type) #Tuple #math.LO #msc:03B30 #msc:03F35
paper · pdf · doi:10.1017/jsl.2016.10
published as Journal of Symbolic Logic, Volume 81, Issue 4, 2016 · 23 pages; a few changes of references; a corrected description of a result of Patey
arxiv created 2014/08/11 · openalex publication_date 2016/12/01 · arxiv updated 2017/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract We introduce the definability strength of combinatorial principles. In terms of definability strength, a combinatorial principle is strong if solving a corresponding combinatorial problem could help in simplifying the definition of a definable set. We prove that some consequences of Ramsey’s Theorem for colorings of pairs could help in simplifying the definitions of some \rmΔ 20 sets, while some others could not. We also investigate some consequences of Ramsey’s Theorem for colorings of longer tuples. These results of definability strength have some interesting consequences in reverse mathematics, including strengthening of known theorems in a more uniform way and also new theorems.