论文标题
阶段中的融合学理论树
Axiomatization of betweenness in order-theoretic trees
论文作者
论文摘要
树的三元间关系B（x，y，z）表示y在x和z之间的唯一路径上。该概念可以扩展到定义为部分订单的顺序理论树，以便将大于任何节点的节点组成线性排序。在这样的广义树中，两个节点之间的独特“路径”可以无限地具有许多节点。 我们概括了在上一篇文章中获得的一些结果，以介绍结合树的之间。联接树是订单理论树，因此任何两个节点都具有最小的上限。动机是方便地定义可数图的排名宽度。我们将Quasi-Tree称为基于联接树的中间关系的结构。我们证明了准树是通过一阶句子进行的。 在这里，我们获得了有序理论树中的中间性的二阶二阶公理化。我们还定义并比较了几种引起的中间关系，即，在不同种类的广义树中对中间关系的节点的限制。我们证明，准树中引起的恋爱的特征是一阶句子。证明使用订单理论树。
The ternary betweenness relation of a tree, B(x,y,z) expresses that y is on the unique path between x and z. This notion can be extended to order-theoretic trees defined as partial orders such that the set of nodes larger than any node is linearly ordered. In such generalized trees, the unique "path" between two nodes can have infinitely many nodes. We generalize some results obtained in a previous article for the betweenness of join-trees. Join-trees are order-theoretic trees such that any two nodes have a least upper-bound. The motivation was to define conveniently the rank-width of a countable graph. We called quasi-tree the structure based on the betweenness relation of a join-tree. We proved that quasi-trees are axiomatized by a first-order sentence. Here, we obtain a monadic second-order axiomatization of betweenness in order-theoretic trees. We also define and compare several induced betweenness relations, i.e., restrictions to sets of nodes of the betweenness relations in generalized trees of different kinds. We prove that induced betweenness in quasi-trees is characterized by a first-order sentence. The proof uses order-theoretic trees.
