Countable Ordinals and Big Ramsey Degrees

Abstract

In this paper we consider big Ramsey degrees of finite chains in countable ordinals. We prove that a countable ordinal has finite big Ramsey degrees if and only if it is smaller than ωω. Big Ramsey degrees of finite chains in all other countable ordinals are infinite.

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Acknowledgements

We would like to thank F. Galvin and S. Todorčević for their help and many insightful observations that led us to the solution of the problem for all countable ordinals.

The first author gratefully acknowledges the support of the Grant No. 174019 of the Ministry of Education, Science and Technological Development of the Republic of Serbia.

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Correspondence to Dragan Mašulović.

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Mašulović, D., Šobot, B. Countable Ordinals and Big Ramsey Degrees. Combinatorica 41, 425–446 (2021). https://doi.org/10.1007/s00493-020-4192-z

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Mathematics Subject Classification (2010)

  • 05D10
  • 03E10