Reverse mathematics and a Ramsey-type König's Lemma

DOI10.2178/jsl.7704120zbMath1259.03022arXiv1111.2526OpenAlexW2038076484WikidataQ124918191 ScholiaQ124918191MaRDI QIDQ4899173

Stephen Flood

Publication date: 7 January 2013

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

Full work available at URL: https://arxiv.org/abs/1111.2526

zbMATH Keywords

reverse mathematicsweak König's lemmaRamsey's theorem for pairs

Mathematics Subject Classification ID

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

Related Items (12)

The proof-theoretic strength of Ramsey's theorem for pairs and two colors ⋮ OPEN QUESTIONS ABOUT RAMSEY-TYPE STATEMENTS IN REVERSE MATHEMATICS ⋮ Primitive recursive reverse mathematics ⋮ Ramsey-type graph coloring and diagonal non-computability ⋮ The Paris-Harrington principle and second-order arithmetic -- bridging the finite and infinite Ramsey theorem ⋮ Separating principles below ⋮ Degrees bounding principles and universal instances in reverse mathematics ⋮ On the logical strengths of partial solutions to mathematical problems ⋮ Ordinals and graph decompositions ⋮ COMPUTABILITY THEORY, NONSTANDARD ANALYSIS, AND THEIR CONNECTIONS ⋮ Pigeons do not jump high ⋮ A packed Ramsey’s theorem and computability theory

Cites Work

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• Stable Ramsey's theorem and measure
• On the strength of Ramsey's theorem
• On the strength of Ramsey's theorem for pairs
• A Δ₂⁰ set with no infinite low subset in either it or its complement
• On the role of the collection principle for Σ⁰₂-formulas in second-order reverse mathematics
• Effective presentability of Boolean algebras of Cantor-Bendixson rank 1
• A cohesive set which is not high

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