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A Classification of Countable Lower 1-transitive Linear Orders

Barbina, Silvia and Chicot, Katie (2017). A Classification of Countable Lower 1-transitive Linear Orders. Order (Early Access).

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DOI (Digital Object Identifier) Link: https://doi.org/10.1007/s11083-017-9427-2
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Abstract

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: 28 Jun 2017 13:15
URI: http://oro.open.ac.uk/id/eprint/49858
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