The strength of the rainbow Ramsey Theorem

DOI10.2178/jsl/1254748693zbMath1188.03044OpenAlexW2157945276MaRDI QIDQ3655258

Joseph R. Mileti, Barbara F. Csima

Publication date: 7 January 2010

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2178/jsl/1254748693

zbMATH Keywords

rainbowstableRCArandom realanti-RamseyCOHhyperimmuneRamsey's TheoremSADSRT2-random

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) Algorithmic randomness and dimension (03D32)

Related Items (17)

Rainbow Ramsey simple structures ⋮ Some remarks on uncountable rainbow Ramsey theory ⋮ Partial Orders and Immunity in Reverse Mathematics ⋮ RAMSEY-LIKE THEOREMS AND MODULI OF COMPUTATION ⋮ Iterative Forcing and Hyperimmunity in Reverse Mathematics ⋮ NONSTANDARD MODELS IN RECURSION THEORY AND REVERSE MATHEMATICS ⋮ Cohesive sets and rainbows ⋮ OPEN QUESTIONS ABOUT RAMSEY-TYPE STATEMENTS IN REVERSE MATHEMATICS ⋮ RANDOMNESS NOTIONS AND REVERSE MATHEMATICS ⋮ Controlling iterated jumps of solutions to combinatorial problems ⋮ 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 \(\text{RT}_2^2\) ⋮ Algorithmic randomness, reverse mathematics, and the dominated convergence theorem ⋮ On uniform relationships between combinatorial problems ⋮ Pigeons do not jump high

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• Combinatorial principles weaker than Ramsey's Theorem for pairs
• The canonical Ramsey theorem and computability theory
• Class groups of integral group rings

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