Effectiveness of Hindman’s Theorem for Bounded Sums

DOI10.1007/978-3-319-50062-1_11zbMath1480.03005arXiv1603.08249OpenAlexW2962772396MaRDI QIDQ2970955

Carl G. jun. Jockusch, Damir D. Dzhafarov, Linda Brown Westrick, D. Reed Solomon

Publication date: 4 April 2017

Published in: Computability and Complexity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.08249

zbMATH Keywords

reverse mathematicsRamsey's theoremHindman's theoremcomputable combinatorics

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 (7)

Hindman's theorem for sums along the full binary tree, \(\Sigma^0_2\)-induction and the pigeonhole principle for trees ⋮ Finiteness classes arising from Ramsey-theoretic statements in set theory without choice ⋮ “Weak yet strong” restrictions of Hindman’s Finite Sums Theorem ⋮ A weak variant of Hindman's theorem stronger than Hilbert's theorem ⋮ New bounds on the strength of some restrictions of Hindman's theorem ⋮ Thin set versions of Hindman's theorem ⋮ Restrictions of Hindman's theorem: an overview

Cites Work

• A simple proof and some difficult examples for Hindman's theorem
• Finite sums from sequences within cells of a partition of N
• A short proof of Hindman's theorem
• On the strength of Ramsey's theorem for pairs
• Probabilistic Constructions of Computable Objects and a Computable Version of Lovász Local Lemma
• On the role of the collection principle for Σ⁰₂-formulas in second-order reverse mathematics
• Ultrafilters: Some old and some new results
• Open Problems in Partition Regularity
• Ramsey's theorem and recursion theory
• Unnamed Item

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