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arXiv · 2203.10293

A note on the Canonical Ramsey Theorem and Ramsey ultrafilters

N. L. Polyakov
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Abstract

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

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N. L. Polyakov. 2022-03-24. A note on the Canonical Ramsey Theorem and Ramsey ultrafilters. https://arxiv.org/abs/2203.10293

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