(In)dependence of the axioms of Λ-trees

Pub Date : 2024-04-01 DOI:10.1515/agms-2023-0106

Raphael Appenzeller

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引用次数: 0

Abstract

\Lambda

-tree is a

\Lambda

-metric space satisfying three axioms (1), (2), and (3). We give a characterization of those ordered abelian groups

\Lambda

for which axioms (1) and (2) imply axiom (3). As a special case, it follows that for the important class of ordered abelian groups

\Lambda

that satisfy

Λ = 2 Λ

\Lambda =2\Lambda

, (3) follows from (1) and (2). For some ordered abelian groups

\Lambda

, we show that axiom (2) is independent of axioms (1) and (3) and ask whether this holds for all ordered abelian groups. Part of this work has been formalized in the proof assistant

Lean

{\mathsf{Lean}}

查看原文

(Λ树公理的（不）依赖性

一个Λ \Lambda 树是一个满足三个公理（1）、（2）和（3）的Λ \Lambda 度量空间。我们给出了公理（1）和（2）意味着公理（3）的有序无边群Λ \Lambda的特征。作为一个特例，对于满足Λ = 2 Λ \Lambda =2 \Lambda 的有序边群Λ \Lambda 这一类重要的有序边群，公理(3)是由公理(1)和(2)得出的。对于某些有序无边群Λ \Lambda ，我们证明公理(2)与公理(1)和(3)无关，并询问这是否对所有有序无边群都成立。这项工作的一部分已经在证明助手 Lean {mathsf{Lean} 中正式化了。｝ .

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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