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Barbina, Silvia and Chicot, Katie
(2018).
DOI: https://doi.org/10.1007/s11083-017-9427-2
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.
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About
- Item ORO ID
- 49858
- Item Type
- Journal Item
- ISSN
- 1572-9273
- Project Funding Details
-
Funded Project Name Project ID Funding Body Not Set EP/H00677X/1 EPSRC - Keywords
- countable linear order; transitive tree; lower 1-transitivity; classification
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2017 The Authors
- Depositing User
- Silvia Barbina