具有无界路径的树的有界初等扩张
Bounded elementary extensions of trees with unbounded paths
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中文总结 AI 辅助
研究具有无界路径的树如何能初等嵌入有界树，确定了充分条件，给出树运算并证明其费弗曼 - 沃特风格保持性质，为相关计算系统建模提供理论支持。
中文摘要 AI 辅助
树是向下线性且向下连通的偏序集。当树的每条路径（即最大线性有序子集）都包含最大元素时，该树称为有界树。在有界树中，每条路径都可以用一阶公式以路径的叶为参数来定义。有界树可用于对诸如芝诺机等计算系统进行建模，其中路径的叶表示无限长计算序列收敛到的状态，或分配给循环计算序列的状态。我们确定了一个充分条件，在该条件下某些无界树可以初等嵌入到有界树中。还给出了几种树运算，并证明了这些运算的费弗曼 - 沃特风格的保持性质。
英文摘要
A tree is a partially ordered set that is downwards linear and downwards connected. A tree is called bounded when each of its paths (i.e. maximal linearly ordered subsets) contains a greatest element. In a bounded tree, each path can be defined by a first-order formula using the leaf of the path as parameter. Bounded trees can be used to model computational systems such as Zeno machines whereby the leaf of a path represents the state to which an infinitely long sequence of computations converges, or a state that is assigned to a computational sequence that loops. We identify a sufficient condition under which certain trees that are not bounded, can be elementarily embedded in trees that are bounded. Several tree operations are also given, and Feferman-Vaught style preservation properties for these operations are proved.
