English

Countable ordinals and big Ramsey degrees

Combinatorics 2019-07-29 v2

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\omega^\omega. Big Ramsey degrees of finite chains in all other countable ordinals are infinite.

Keywords

Cite

@article{arxiv.1904.03637,
  title  = {Countable ordinals and big Ramsey degrees},
  author = {Dragan Mašulović and Branislav Šobot},
  journal= {arXiv preprint arXiv:1904.03637},
  year   = {2019}
}