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On a question of Andreas Weiermann
Mathematical Logic Quarterly 55 (2):201-211 (2009)
Abstract
We prove that for each β, γ < ε0 there existsα < ε0 such that whenever A ⊆ ω is α ‐large and G: A → β is such that (∀a ∈ A)(psn(G (a)) ≤ a), then there exists a γ ‐large C ⊆ A on which G is nondecreasing. Moreover, we give upper bounds for α for small ordinals β ≤ ω (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)My notes
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References found in this work
On the strength of Ramsey's theorem for pairs.Peter A. Cholak, Carl G. Jockusch & Theodore A. Slaman - 2001 - Journal of Symbolic Logic 66 (1):1-55.
Combinatorial principles weaker than Ramsey's Theorem for pairs.Denis R. Hirschfeldt & Richard A. Shore - 2007 - Journal of Symbolic Logic 72 (1):171-206.
A Uniform Approach to Fundamental Sequences and Hierarchies.Wilfried Buchholz, Adam Cichon & Andreas Weiermann - 1994 - Mathematical Logic Quarterly 40 (2):273-286.
The strength of infinitary Ramseyan principles can be accessed by their densities.Andrey Bovykin & Andreas Weiermann - 2017 - Annals of Pure and Applied Logic 168 (9):1700-1709.
On the strength of Ramsey's theorem for pairs.Peter A. Cholak, Carl G. Jockusch & Theodore A. Slaman - 2001 - Journal of Symbolic Logic 66 (1):1-55.
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