Cohesive sets and rainbows

DOI10.1016/j.apal.2013.06.002zbMath1300.03012arXiv1303.3329OpenAlexW2160285120MaRDI QIDQ386619

Wei Wang

Publication date: 10 December 2013

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.3329

zbMATH Keywords

reverse mathematicsRamsey's theoremweak König's lemmaWKLcohesive setrainbow Ramsey theorem

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) Ramsey theory (05D10) Applications of computability and recursion theory (03D80) Second- and higher-order arithmetic and fragments (03F35) Hierarchies of computability and definability (03D55)

Related Items (10)

OPEN QUESTIONS ABOUT RAMSEY-TYPE STATEMENTS IN REVERSE MATHEMATICS ⋮ The coding power of a product of partitions ⋮ Controlling iterated jumps of solutions to combinatorial problems ⋮ THE DEFINABILITY STRENGTH OF COMBINATORIAL PRINCIPLES ⋮ Some logically weak Ramseyan theorems ⋮ Degrees bounding principles and universal instances in reverse mathematics ⋮ The weakness of the pigeonhole principle under hyperarithmetical reductions ⋮ Combinatorial principles between \(\text{RRT}_2^2\) and \(\text{RT}_2^2\) ⋮ \( \mathsf{SRT}_2^2\) does not imply \(\mathsf{RT}_2^2\) in \(\omega \)-models ⋮ Pigeons do not jump high

Cites Work

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• On the strength of Ramsey's theorem
• On the strength of Ramsey's theorem for pairs
• Rainbow Ramsey Theorem for Triples is Strictly Weaker than the Arithmetical Comprehension Axiom
• RT₂² does not imply WKL₀
• Combinatorial principles weaker than Ramsey's Theorem for pairs
• The strength of the rainbow Ramsey Theorem
• A cohesive set which is not high
• ∏ 0 1 Classes and Degrees of Theories
• Ramsey's theorem and recursion theory

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