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 \(\textbf{0}\) $\mathbf{0}$ , \(\textbf{1}\) $\mathbf{1}$ , and that is closed under isomorphisms, finite order sum, anti-lexicographic product with \(\omega \) $\omega$ and \(\omega ^*\) ${\omega }^{\ast }$ , 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 \(\mathbb {N}\) $\mathbb{N}$ -strings in the completion of hammocks.