The closed ordinal Ramsey number 𝑅^{𝑐𝑙}(𝜔²,3)=𝜔⁶

Mermelstein, Omer

doi:10.1090/proc/14697

The closed ordinal Ramsey number $R^{cl}(\omega ^2,3) = \omega ^6$
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Proc. Amer. Math. Soc. 148 (2020), 413-419 Request permission

Abstract:

Closed ordinal Ramsey numbers are a topological variant of the classical (ordinal) Ramsey numbers. We compute the exact value of the closed ordinal Ramsey number $R^{cl}(\omega ^2,3) = \omega ^6$.

References

James E. Baumgartner, Partition relations for countable topological spaces, J. Combin. Theory Ser. A 43 (1986), no. 2, 178–195. MR 867644, DOI 10.1016/0097-3165(86)90059-2
Andrés Eduardo Caicedo and Jacob Hilton, Topological Ramsey numbers and countable ordinals, Foundations of mathematics, Contemp. Math., vol. 690, Amer. Math. Soc., Providence, RI, 2017, pp. 87–120. MR 3656308, DOI 10.1090/conm/690
P. Erdös and R. Rado, A partition calculus in set theory, Bull. Amer. Math. Soc. 62 (1956), 427–489. MR 81864, DOI 10.1090/S0002-9904-1956-10036-0
Jacob Hilton, The topological pigeonhole principle for ordinals, J. Symb. Log. 81 (2016), no. 2, 662–686. MR 3519451, DOI 10.1017/jsl.2015.45
András Hajnal and Jean A. Larson, Partition relations, Handbook of set theory. Vols. 1, 2, 3, Springer, Dordrecht, 2010, pp. 129–213. MR 2768681, DOI 10.1007/978-1-4020-5764-9_{3}
Omer Mermelstein, Calculating the closed ordinal Ramsey number $R^{cl}(\omega \cdot 2, 3)$, Israel J. Math. 230 (2019), no. 1, 387–407. MR 3941152, DOI 10.1007/s11856-019-1827-0
Diana Ojeda-Aristizabal and William Weiss, Topological partition relations for countable ordinals, Fund. Math. 244 (2019), no. 2, 147–166. MR 3874669, DOI 10.4064/fm413-1-2018
C. Piña, A topological Ramsey classification of countable ordinals, Acta Math. Hungar. 147 (2015), no. 2, 477–509. MR 3420590, DOI 10.1007/s10474-014-0413-5
Ernst Specker, Teilmengen von Mengen mit Relationen, Comment. Math. Helv. 31 (1957), 302–314 (German). MR 88454, DOI 10.1007/BF02564361