2022/03/19 by N. L. Polyakov, Polyakov, N. L.
Mathematics · #Advanced Topology and Set Theory #Limits and Structures in Graph Theory #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2203.10293
We give a characterizations of Ramsey ultrafilters on \mathscr P(ω) in terms of functions f:ωn→ω 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⊆ ω that is homogeneous for \mathcal Q is a finite union of sets that are canonical for \mathcal P.