On the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs without AC

2024/01/04 by Amitayu Banerjee, Banerjee, Amitayu, Alexa Gopaulsingh +3
Computer Science · Mathematics · #03E25 03E35 06A07 #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2401.02215

openalex publication_date 2024/01/04 · openalex created_date 2024/01/10 · openalex updated_date 2026/07/28

Abstract

In set theory without the Axiom of Choice, we study the set-theoretic strength of a generalized version of the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs introduced by Erdős and Rado, concerning their interrelation with several weak choice forms.

Related

• Somewhere over the rainbow Ramsey theorem for pairs
• Weaker cousins of Ramsey's theorem over a weak base theory
• Comparisons of polychromatic and monochromatic Ramsey theory
• Coloring the rationals in reverse mathematics
• A Rainbow Ramsey Analogue of Rado's Theorem