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

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅存取

详细

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 \(\mathcal{P}\).

作者简介

N. Polyakov

HSE University

编辑信件的主要联系方式.
Email: npolyakov@hse.ru
Russia, Moscow

参考

  1. Ramsey F.P. On a problem of formal logic // Proc. London Math. Soc. 1930. V. 30. P. 264–286.
  2. Matet P. An easier proof of the Canonical Ramsey Theorem // Colloquium Mathematicum. 2016, 216. V. 145. P. 187–191.
  3. Erdős P., Rado R. A combinatorial theorem // J. London Math. Soc. 1950. V. 25. P. 249–255.
  4. Rado R. Note on Canonical Partitions // Bul. of the London Math. Soc. 1986. V. 18:2. P. 123–126.
  5. Mileti J. R. The canonical Ramsey theorem and computability theory // Trans. Amer. Math. Soc. 2008. V. 360. P. 1309–1341.
  6. Erdős P., Rado R. Combinatorial Theorems on Classifications of Subsets of a Given Set // Proc. London Math. Soc. 1952. V. s3–2:1. P. 417–439.
  7. Lefmann H., Rödl V. On Erdős-Rado numbers // Combinatorica. 1995. V. 15. P. 85–104.
  8. Comfort W.W., Negrepontis S. The theory of ultrafilters. Springer, Berlin, 1974.
  9. Jeh T. Set theory. The Third Millennium Edition, revised and expanded. Springer, 2002.
  10. Graham R.L., Rothschild B.L., Spencer J.H. Ramsey Theory. 2rd ed. John Wiley and Sons, NY, 1990.
  11. Goranko V. Filter and ultrafilter extensions of structures: universal-algebraic aspects. Preprint, 2007.
  12. Saveliev D.I. Ultrafilter extensions of models // LNCS. 2011. V. 6521. P. 162–177.
  13. Jeh T. Lectures in Set Theory: With Particular Emphasis on the Method of Forcing. Springer-Verlag. 1971. Русский перевод: Йех Т. Теория множеств и метод форсинга. Издательство “Мир”, М., 1973.
  14. Wimmers E. The Shelah P-point independence theorem // Israel Journal of Mathematics. 1982. V. 43:1. P. 28–48.
  15. Hindman N., Strauss D. Algebra in the Stone–Čech Compactification. 2nd ed., revised and expanded, W. de Gruyter, Berlin–N.Y., 2012.
  16. Polyakov N.L., Shamolin M.V. On a generalization of Arrow’s impossibility theorem // Dokl. Math. 2014. V. 89. P. 290–292.
  17. Saveliev D.I. On ultrafilter extensions of models // In: S.-D. Friedman et al. (eds.). The Infinity Project Proc. CRM Documents 11, Barcelona, 2012. P. 599–616.
  18. Saveliev D.I. On idempotents in compact left topological universal algebras // Topology Proc. 2014. V. 43. P. 37–46.
  19. Poliakov N.L., Saveliev D.I. On two concepts of ultrafilter extensions of first-order models and their generalizations // LNCS. 2017. V. 10388. P. 336–348.
  20. Poliakov N.L., Saveliev D.I. On ultrafilter extensions of first-order models and ultrafilter interpretations // Arch. Math. Logic. 2021. V. 60. P. 625–681.
  21. Saveliev D.I., Shelah S. Ultrafilter extensions do not preserve elementary equivalence // Math. Log. Quart. 2019. V. 65. P. 511–516.

补充文件

附件文件
动作
1. JATS XML

版权所有 © Н.Л. Поляков, 2023