Chicot, KM and Truss, JK (2017) Countable 1-transitive trees. In: Droste, M, Fuchs, L, Goldsmith, B and Strungmann, L, (eds.) Groups, Modules, and Model Theory - Surveys and Recent Developments: In Memory of Rüdiger Göbel. Springer International Publishing ISBN 978-3-319-51717-9
Abstract
We give a survey of three pieces of work, on 2-transitive trees [11], on weakly 2-transitive trees [10], and on lower 1-transitive linear orders [5], all in the countable case. We lead on from these to give a complete description of all the countable 1-transitive trees. In fact the work of [5] was carried out as a preliminary to finding such a description. This is because the maximal chains in any 1-transitive tree are easily seen to be lower 1-transitive, but are not necessarily 1-transitive. In fact a more involved set-up has to be considered, namely a coloured version of the same situation (where ‘colours’ correspond to various types of ramification point), so a major part of what we do here is to describe a large class of countable coloured lower 1-transitive linear orders and go on to use this to complete the description of all countable 1-transitive trees. This final stage involves analyzing how the possible coloured branches can fit together, with particular attention to the possibilities for cones at ramification points.
Metadata
Item Type: | Book Section |
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Authors/Creators: |
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Editors: |
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Keywords: | tree, lower semilinear order, 1-transitive, cone, ramification point, coding tree |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Mar 2018 10:12 |
Last Modified: | 26 Mar 2018 10:12 |
Status: | Published |
Publisher: | Springer International Publishing |
Identification Number: | 10.1007/978-3-319-51718-6 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:128954 |