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An Analysis of Ramsey′s Theorem
Information and Computation, 1994 The main result of this paper may be paraphrased as follows. A collection \(B\) of finite sets of natural numbers is called unavoidable iff every infinite set of natural numbers has a subset in \(B\). Let \(s\) be a fixed natural number, the number of colours.
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Approximate Euclidean Ramsey theorems
Journal of Computational Geometry, 2010 According to a classical result of Szemerédi, every dense subset of 1,2,…,N contains an arbitrary long arithmetic progression, if N is large enough. Its analogue in higher dimensions due to Fürstenberg and Katznelson says that every dense subset of {1,2,…,N}d contains an arbitrary large grid, if N is large enough.
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The proof-theoretic strength of Ramsey's theorem for pairs and two colors [PDF]
, 2016 Ludovic Patey, Keita Yokoyama
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Low-like basis theorems for Ramsey's theorem for pairs in first-order arithmetic [PDF]
Hiroyuki Ikari, Keita Yokoyama
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Assessing and Resolving Model Misspecifications in Metabolic Flux Analysis. [PDF]
Bioengineering (Basel), 2017 Gunawan R, Hutter S.
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Ramsey's Theorem and the Pigeonhole Principle in Intuitionistic Mathematics
, 1993 Wim Veldman, Bezem
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Weaker cousins of Ramsey's theorem over a weak base theory [PDF]
, 2021 Marta Fiori-Carones +2 more
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