Hammocks for non-domestic string algebras

Abstract

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 $0$, $1$, and that is closed under isomorphisms, finite order sum, anti-lexicographic product with $\omega$ and ${\omega }^{\ast }$, 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.

30 pages, 5 figures