The ${\mathrm{\aleph }}_0$-categorical Trees and Cycle-free Partial Orders

We provide a description of the structure of ${\mathrm{\aleph }}_0$-categorical trees and cycle-free partial orders. First the maximal branches of ${\mathrm{\aleph }}_0$-categorical tree are examined, followed by the configuration of the ramification orders, which are then combined to provided necessary and sufficient conditions for a tree to be ${\mathrm{\aleph }}_0$-categorical in terms of these two things. The classification of the ${\mathrm{\aleph }}_0$-categorical cycle-free partial orders is found as a corollary.