By Peter Cholak and Ludovic Patey

The thin set theorem \(\mathsf{RT}^n_{<\infty,\ell}\) asserts the existence, for every \(k\)-coloring of the subsets of natural numbers of size \(n\), of an infinite set of natural numbers, all of whose subsets of size \(n\) use at most \(\ell\) colors. Whenever \(\ell = 1\), the statement corresponds to Ramsey's theorem. From... Show more

March 16, 2019

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Thin set theorems and cone avoidance

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