The $\aleph_{0}$-categorical Trees and Cycle-free Partial Orders

Abstract

We provide a description of the structure of ℵ 0 -categorical trees and cycle-free partial orders. First the maximal branches of ℵ 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 ℵ 0 -categorical in terms of these two things. The classification of the ℵ 0 -categorical cycle-free partial orders is found as a corollary.