On principles between ∑1- and ∑2-induction, and monotone enumerations

DOI10.1142/S0219061316500045zbMath1436.03303arXiv1306.1936MaRDI QIDQ3186059

Alexander P. Kreuzer, Keita Yokoyama

Publication date: 8 August 2016

Published in: Journal of Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.1936

zbMATH Keywords

reverse mathematicsAckermann functionordinal numbersParis-Harrington theorembounded monotone enumerationsfragments of arithmetics

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Foundations of classical theories (including reverse mathematics) (03B30)

Related Items (7)

Minimal bad sequences are necessary for a uniform Kruskal theorem ⋮ On the strength of Ramsey's theorem for trees ⋮ Reverse mathematics of the finite downwards closed subsets of ordered by inclusion and adjacent Ramsey for fixed dimension ⋮ Algebraic combinatorics in bounded induction ⋮ Dickson's lemma and weak Ramsey theory ⋮ Reverse mathematics and colorings of hypergraphs ⋮ In search of the first-order part of Ramsey's theorem for pairs

Cites Work

• Unnamed Item
• The inductive strength of Ramsey's theorem for pairs
• Rapidly growing Ramsey functions
• The strength of infinitary Ramseyan principles can be accessed by their densities
• The metamathematics of Stable Ramsey’s Theorem for Pairs
• Slicing the Truth
• Combinatorial principles concerning approximations of functions
• REVERSE MATHEMATICS, YOUNG DIAGRAMS, AND THE ASCENDING CHAIN CONDITION

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