A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is
We consider classes of arbitrary (finite or infinite) graphs of bounded shrub-depth, specifically the class TM_r, p(d) of p-labeled arbitrary graphs whose underlying unlabeled graphs have tree models of height d and r labels. We show that this class satisfies an extension of the classical Löwenheim-Skolem property into the finite and for MSO. This extension being a generalization of the small model property, we obtain that the graphs of TM_r, p(d) are pseudo-finite. In addition, we obtain asarXiv:2010.05799v1 fatcat:fpco5dvxarfi3pegqogcgxbjym