Countable ordinals and big Ramsey degrees

Published 7 Apr 2019 in math.CO | (1904.03637v2)

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

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