Journal of the Mathematical Society of Japan

Partitioning subsets of generalised scattered orders


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In 1956, 48 years after Hausdorff provided a comprehensive account on ordered sets and defined the notion of a scattered order, Erdős and Rado founded the partition calculus in a seminal paper. The present paper gives an account of investigations into generalisations of scattered linear orders and their partition relations for both singletons and pairs. We consider analogues for these order-types of known partition theorems for ordinals or scattered orders and prove a partition theorem from assumptions about cardinal characteristics. Together, this continues older research by Erdős, Galvin, Hajnal, Larson and Takahashi and more recent investigations by Abraham, Bonnet, Cummings, Džamonja, Komjáth, Shelah and Thompson.

Article information

J. Math. Soc. Japan, Volume 71, Number 1 (2019), 235-257.

Received: 14 August 2017
First available in Project Euclid: 20 November 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E02: Partition relations
Secondary: 03E17: Cardinal characteristics of the continuum 05C63: Infinite graphs 05D10: Ramsey theory [See also 05C55] 06A05: Total order

graph linear order partition relation Ramsey theory scattered order stick unbounding number


LAMBIE-HANSON, Chris; WEINERT, Thilo. Partitioning subsets of generalised scattered orders. J. Math. Soc. Japan 71 (2019), no. 1, 235--257. doi:10.2969/jmsj/78617861.

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