(In)dependence of the axioms of $Λ$-trees
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866929440910475264 |
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| author | Appenzeller, Raphael |
| author_facet | Appenzeller, Raphael |
| contents | 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 the 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 \textsf{Lean}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_02704 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | (In)dependence of the axioms of $Λ$-trees Appenzeller, Raphael Group Theory 51M30 (Primary), 06F20, 05C05 (Secondary) 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 the 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 \textsf{Lean}. |
| title | (In)dependence of the axioms of $Λ$-trees |
| topic | Group Theory 51M30 (Primary), 06F20, 05C05 (Secondary) |
| url | https://arxiv.org/abs/2112.02704 |