(In)dependence of the axioms of Λ-trees

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces 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}}

查看原文本刊更多论文

(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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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.