A Classification of Countable Lower 1-transitive Linear OrdersReport as inadecuate




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pp 1–17

First Online: 27 June 2017Received: 08 November 2015Accepted: 28 April 2017

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, \leqslant \ 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.

KeywordsCountable linear order Transitive tree Lower 1-transitivity Classification The results in this paper form part of the second author’s PhD thesis at the University of Leeds, which was supported by EPSRC grant EP-H00677X-1.

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Author: Silvia Barbina - Katie Chicot

Source: https://link.springer.com/







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