Journal of the Mathematical Society of Japan

Partitioning subsets of generalised scattered orders

Chris LAMBIE-HANSON and Thilo WEINERT

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1542704621

Digital Object Identifier
doi:10.2969/jmsj/78617861

Mathematical Reviews number (MathSciNet)
MR3909920

Zentralblatt MATH identifier
07056563

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

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

Citation

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. https://projecteuclid.org/euclid.jmsj/1542704621


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