关于可数1-传递树的一种分类：可数下1-传递树linear orders
Towards a classification of countable 1-transitive trees: countable lower 1-transitive linear orders
摘要：
本文给出了可数下1-传递线性序的一个分类。下1-传递性的概念推广了线性序的1-传递性的概念，是1-传递树结构理论的基础。分类是根据“编码树”给出的。这些描述了如何从简单的片段使用连接，字典式产品和其他类型的结构来制造线性顺序。我们定义了编码树，并展示了它们如何编码低1-传递线性顺序。然后，我们证明了一个编码树可以恢复从一个低1-传递的线性顺序$(X, \leq)$通过检查所有的不变分区$X$。
英文摘要：
This paper contains a classification of countable lower 1-transitive linear orders. The notion of lower 1-transitivity generalises that of 1-transitivity for linear orders, and is essential for the structure theory of 1-transitive trees. The classification is given in terms of 'coding trees'. These 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 how they encode lower 1-transitive linear orders. Then we show that a coding tree can be recovered from a lower 1-transitive linear order $(X, \leq)$ by examining all the invariant partitions on $X$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
