Partition Theorems and Computability Theory

DOI10.2178/bsl/1122038995zbMath1097.03037OpenAlexW2098052203MaRDI QIDQ3370615

Joseph R. Mileti

Publication date: 8 February 2006

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

Full work available at URL: https://doi.org/10.2178/bsl/1122038995

zbMATH Keywords

surveypartitionRamseyreverse mathematicscomputabilitycanonicalregressive

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) Theory of numerations, effectively presented structures (03D45)

Related Items (15)

The proof-theoretic strength of Ramsey's theorem for pairs and two colors ⋮ On notions of computability-theoretic reduction between Π21 principles ⋮ RAMSEY-LIKE THEOREMS AND MODULI OF COMPUTATION ⋮ Automorphisms of models of arithmetic: a unified view ⋮ Coloring trees in reverse mathematics ⋮ OPEN QUESTIONS ABOUT RAMSEY-TYPE STATEMENTS IN REVERSE MATHEMATICS ⋮ Weakly Represented Families in Reverse Mathematics ⋮ Some Questions in Computable Mathematics ⋮ 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 ⋮ \( \mathsf{SRT}_2^2\) does not imply \(\mathsf{RT}_2^2\) in \(\omega \)-models ⋮ The polarized Ramsey's theorem ⋮ Pigeons do not jump high

Cites Work

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• On Gödel incompleteness and finite combinatorics
• 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
• Note on Canonical Partitions
• Generalized cohesiveness
• A cohesive set which is not high
• Effective versions of Ramsey's Theorem: Avoiding the cone above 0′
• Class groups of integral group rings
• Ramsey's theorem and recursion theory

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