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

Abstract

We provide a description of the structure of ${\aleph }_0$-categorical trees and cycle-free partial orders. First the maximal branches of ${\aleph }_0$-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 ${\aleph }_0$-categorical in terms of these two things. The classification of the ${\aleph }_0$-categorical cycle-free partial orders is found as a corollary.

13 pages, 1 figure

References in corpus (1)

• The Reconstruction of Cycle-free Partial Orders from their Abstract Automorphism Groups III : Decorated CFPOs