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Author
Date
2024-01Type
- Journal Article
ETH Bibliography
yes
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Abstract
A Λ-tree is a Λ-metric space satisfying three axioms (1), (2), and (3). We give a characterization of those ordered abelian groups Λ for which axioms (1) and (2) imply axiom (3). As a special case, it follows that for the important class of ordered abelian groups Λ that satisfy Λ = 2Λ, (3) follows from (1) and (2). For some ordered abelian groups Λ, 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. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000668653Publication status
publishedExternal links
Journal / series
Analysis and Geometry in Metric SpacesVolume
Pages / Article No.
Publisher
De GruyterSubject
Λ-trees; ordered abelian groups; Euclidean fields; Λ-buildingsRelated publications and datasets
Is new version of: https://doi.org/10.3929/ethz-b-000588445
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ETH Bibliography
yes
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