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A Classification of Countable Lower 1-transitive Linear Orders

Barbina, Silvia and Chicot, Katie (2018). A Classification of Countable Lower 1-transitive Linear Orders. Order, 35(2) pp. 215–231.

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This paper contains a classification of countable lower 1-transitive linear orders. This is the first step in the classification of countable 1-transitive trees given in Chicot and Truss (2009): the notion of lower 1-transitivity generalises that of 1-transitivity for linear orders, and it is essential for the structure theory of 1-transitive trees. The classification is given in terms of coding trees, which describe how a linear order is fabricated from simpler pieces using concatenations, lexicographic products and other kinds of construction. We define coding trees and show that a coding tree can be constructed from a lower 1-transitive linear order (X,≤) by examining all the invariant partitions on X. Then we show that a lower 1-transitive linear order can be recovered from a coding tree up to isomorphism.

Item Type: Journal Item
Copyright Holders: 2017 The Authors
ISSN: 1572-9273
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetEP/H00677X/1EPSRC
Keywords: countable linear order; transitive tree; lower 1-transitivity; classification
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 49858
Depositing User: Silvia Barbina
Date Deposited: 28 Jun 2017 13:05
Last Modified: 01 May 2019 12:22
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