SEPARATING PRINCIPLES BELOW RAMSEY'S THEOREM FOR PAIRS

DOI10.1142/S0219061313500074zbMath1326.03021arXiv1302.0828MaRDI QIDQ5401600

Henry Towsner, Manuel Lerman, D. Reed Solomon

Publication date: 10 March 2014

Published in: Journal of Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.0828

zbMATH Keywords

iterated forcingreverse mathematicsCACRamsey's theorem for pairsADSErdős-Moser theorem

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) Second- and higher-order arithmetic and fragments (03F35)

Related Items (26)

An inside/outside Ramsey theorem and recursion theory ⋮ Reverse mathematical bounds for the termination theorem ⋮ The proof-theoretic strength of Ramsey's theorem for pairs and two colors ⋮ Partial Orders and Immunity in Reverse Mathematics ⋮ RELATIONSHIPS BETWEEN COMPUTABILITY-THEORETIC PROPERTIES OF PROBLEMS ⋮ THE REVERSE MATHEMATICS OF THE THIN SET AND ERDŐS–MOSER THEOREMS ⋮ Iterative Forcing and Hyperimmunity in Reverse Mathematics ⋮ The uniform content of partial and linear orders ⋮ Dominating the Erdős-Moser theorem in reverse mathematics ⋮ Extracting randomness within a subset is hard ⋮ OPEN QUESTIONS ABOUT RAMSEY-TYPE STATEMENTS IN REVERSE MATHEMATICS ⋮ Ramsey’s theorem for singletons and strong computable reducibility ⋮ Ramsey-type graph coloring and diagonal non-computability ⋮ Separating principles below ⋮ Some upper bounds on ordinal-valued Ramsey numbers for colourings of pairs ⋮ Controlling iterated jumps of solutions to combinatorial problems ⋮ (EXTRA)ORDINARY EQUIVALENCES WITH THE ASCENDING/DESCENDING SEQUENCE PRINCIPLE ⋮ THE STRENGTH OF THE TREE THEOREM FOR PAIRS IN REVERSE MATHEMATICS ⋮ THE DEFINABILITY STRENGTH OF COMBINATORIAL PRINCIPLES ⋮ The Reverse Mathematics of wqos and bqos ⋮ Weaker cousins of Ramsey's theorem over a weak base theory ⋮ Degrees bounding principles and universal instances in reverse mathematics ⋮ On the logical strengths of partial solutions to mathematical problems ⋮ The weakness of being cohesive, thin or free in reverse mathematics ⋮ On uniform relationships between combinatorial problems ⋮ Constructing sequences one step at a time

Cites Work

• Primitive recursion and the chain antichain principle
• On the strength of Ramsey's theorem for pairs
• Combinatorial principles weaker than Ramsey's Theorem for pairs
• The atomic model theorem and type omitting

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