ON THE CANONICAL RAMSEY THEOREM OF ERDŐS AND RADO AND RAMSEY ULTRAFILTERS

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Abstract

We give a characterizations of Ramsey ultrafilters on ω in terms of functions \(f:{{\omega }^{n}} \to \omega \) and their ultrafilter extensions. To do this, we prove that for any partition \(\mathcal{P}\) of \({{[\omega ]}^{n}}\) there is a finite partition \(\mathcal{Q}\) of \({{[\omega ]}^{{2n}}}\) such that any set \(X \subseteq \omega \) that is homogeneous for \(\mathcal{Q}\) is a finite union of sets that are canonical for \(\mathcal{P}\).

About the authors

N. L. Polyakov

HSE University

Author for correspondence.
Email: npolyakov@hse.ru
Russia, Moscow

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