2012/01/05 by Stephen Fenner, Fenner, Stephen, William Gasarch +1
Computer Science · Mathematics · #03-01 #05-01 #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO #msc:03-01 #msc:05-01
paper · pdf · doi:10.48550/arxiv.1201.1207
12 pages
arxiv created 2012/01/05 · openalex publication_date 2012/01/05 · arxiv updated 2012/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that, for any finite coloring of the naturals, there exists distinct naturals e1,e2,e3,e4 that are the same color such that e1+e2=e3+e4. Consider the following statement which we denote S: For every ℵ0-coloring of the reals there exists distinct reals e1,e2,e3,e4 such that e1+e2=e3+e4? Is it true? Erdos showed that S is equivalent to the negation of the Continuum Hypothesis, and hence S is indepedent of ZFC. We give an exposition of his proof and some modern observations about results of this sort.