Open Access
January, 2019 Partitioning subsets of generalised scattered orders
J. Math. Soc. Japan 71(1): 235-257 (January, 2019). DOI: 10.2969/jmsj/78617861


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.


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Chris LAMBIE-HANSON. Thilo WEINERT. "Partitioning subsets of generalised scattered orders." J. Math. Soc. Japan 71 (1) 235 - 257, January, 2019.


Received: 14 August 2017; Published: January, 2019
First available in Project Euclid: 20 November 2018

zbMATH: 07056563
MathSciNet: MR3909920
Digital Object Identifier: 10.2969/jmsj/78617861

Primary: 03E02
Secondary: 03E17 , 05C63 , 05D10 , 06A05

Keywords: graph , linear order , partition relation , Ramsey theory , scattered order , stick , unbounding number

Rights: Copyright © 2019 Mathematical Society of Japan

Vol.71 • No. 1 • January, 2019
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