On the strength of Ramsey's theorem for trees

DOI10.1016/J.AIM.2020.107180zbMath1444.03012OpenAlexW3023701676MaRDI QIDQ2182273

Yanyan Li

Publication date: 23 May 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2020.107180

zbMATH Keywords

reverse mathematicsAckermann function\(\Pi_1^1\)-conservation\(P \Sigma_1^0\)\(TT^1\)Ramsey's theorem for trees

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 (3)

Hindman's theorem for sums along the full binary tree, \(\Sigma^0_2\)-induction and the pigeonhole principle for trees ⋮ On the computability of perfect subsets of sets with positive measure ⋮ The strength of Ramsey’s theorem for pairs over trees: I. Weak König’s Lemma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(\varPi^1_1\)-conservation of combinatorial principles weaker than Ramsey's theorem for pairs
• The inductive strength of Ramsey's theorem for pairs
• The proof-theoretic strength of Ramsey's theorem for pairs and two colors
• On the strength of Ramsey's theorem
• Coloring trees in reverse mathematics
• Some logically weak Ramseyan theorems
• On the strength of Ramsey's theorem for pairs
• RT₂² does not imply WKL₀
• NONSTANDARD MODELS IN RECURSION THEORY AND REVERSE MATHEMATICS
• On principles between ∑1- and ∑2-induction, and monotone enumerations
• The metamathematics of Stable Ramsey’s Theorem for Pairs
• Reverse mathematics, computability, and partitions of trees
• Reverse mathematics and Ramsey's property for trees
• The jump of a Σ _n -cut

This page was built for publication: On the strength of Ramsey's theorem for trees