“Weak yet strong” restrictions of Hindman’s Finite Sums Theorem

DOI10.1090/proc/13856zbMath1477.03174arXiv1610.07500OpenAlexW2543836030MaRDI QIDQ4596010

Lorenzo Carlucci

Publication date: 8 December 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.07500

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)

Hindman's theorem for sums along the full binary tree, \(\Sigma^0_2\)-induction and the pigeonhole principle for trees ⋮ A note on Hindman-type theorems for uncountable cardinals ⋮ A weak variant of Hindman's theorem stronger than Hilbert's theorem ⋮ New Hindman spaces ⋮ Restrictions of Hindman's theorem: an overview

Cites Work

• Hilbert versus Hindman
• Finite sums from sequences within cells of a partition of N
• On the strength of Ramsey's theorem for pairs
• Effectiveness of Hindman’s Theorem for Bounded Sums
• Open Questions in Reverse Mathematics
• Slicing the Truth
• Primitive Recursive Bounds for Van Der Waerden Numbers
• Open Problems in Partition Regularity
• Brown’s lemma in second-order arithmetic
• Ramsey Theory for Discrete Structures
• The Existence of Certain Ultrafilters on N and a Conjecture of Graham and Rothschild
• Ramsey's theorem and recursion theory
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