Authors: Di Prisco, Carlos
Todorčević, Stevo 
Title: The shift graph and the Ramsey degree of ℕ ω
Journal: Acta Mathematica Hungarica
Volume: 142
Issue: 2
First page: 484
Last page: 493
Issue Date: 1-Apr-2014
Rank: M23
ISSN: 0236-5294
DOI: 10.1007/s10474-013-0349-1
Abstract: 
We address several questions related to the Ramsey degree of the class of infinite structures isomorphic to the positive integers with the usual ordering. In particular we study the strength of stating that this class has finite Ramsey degree in the absence of the axiom of choice. We show that if the shift graph has finite chromatic number then this class has infinite Ramsey degree.
Keywords: 03E02 | 03E05 | non-meager filter | partition relation | Ramsey degree | shift graph
Publisher: Springer Link

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