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:ωn→ω and their ultrafilter extensions. To do this, we prove that for any partition P of [ω]n there is a finite partition Q of [ω]2n such that any set X⊆ω that is homogeneous for Q is a finite union of sets that are canonical for P.

About the authors

N. L. Polyakov

HSE University

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

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