Hammocks for non-domestic string algebras
We show that the order type of the simplest version of a hammock for string algebras lies in the class of finite description linear orders--the smallest class of linear orders containing $\mathbf 0$, $\mathbf 1$, and that is closed under isomorphisms, finite order sum, anti-lexicographic product wit...
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Zusammenfassung: | We show that the order type of the simplest version of a hammock for string
algebras lies in the class of finite description linear orders--the smallest
class of linear orders containing $\mathbf 0$, $\mathbf 1$, and that is closed
under isomorphisms, finite order sum, anti-lexicographic product with $\omega$
and $\omega^*$, and shuffle of finite subsets--using condensation
(localization) of linear orders as a tool. We also introduce two finite subsets
of the set of bands and use them to describe the location of left $\mathbb
N$-strings in the completion of hammocks. |
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DOI: | 10.48550/arxiv.2301.05956 |