The thin set theorem for pairs implies DNR

DOI10.1215/00294527-3153606zbMath1372.03028OpenAlexW1889875823MaRDI QIDQ894259

Brian Rice

Publication date: 30 November 2015

Published in: Notre Dame Journal of Formal Logic (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ndjfl/1443620509

zbMATH Keywords

reverse mathematicsRamsey's theoremthin set

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)

Related Items (5)

RELATIONSHIPS BETWEEN COMPUTABILITY-THEORETIC PROPERTIES OF PROBLEMS ⋮ Iterative Forcing and Hyperimmunity in Reverse Mathematics ⋮ Degrees bounding principles and universal instances in reverse mathematics ⋮ The weakness of the pigeonhole principle under hyperarithmetical reductions ⋮ Pigeons do not jump high

Cites Work

• Unnamed Item
• \(\varPi^1_1\)-conservation of combinatorial principles weaker than Ramsey's theorem for pairs
• On the strength of Ramsey's theorem
• Some logically weak Ramseyan theorems
• On the density of families of sets
• On the strength of Ramsey's theorem for pairs
• RT₂² does not imply WKL₀
• Combinatorial principles weaker than Ramsey's Theorem for pairs
• The Strength of Some Combinatorial Principles Related to Ramsey's Theorem for Pairs
• The atomic model theorem and type omitting

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