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ON THE CANONICAL RAMSEY THEOREM OF ERDŐS AND RADO AND RAMSEY ULTRAFILTERS
- Authors: Polyakov N.L.1
-
Affiliations:
- HSE University
- Issue: Vol 513, No 1 (2023)
- Pages: 76-87
- Section: MATHEMATICS
- URL: https://journals.rcsi.science/2686-9543/article/view/247072
- DOI: https://doi.org/10.31857/S2686954323600805
- EDN: https://elibrary.ru/CKOEZZ
- ID: 247072
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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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