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

Robert Barham

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arXiv · 1503.03336

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

Robert Barham

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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.

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Robert Barham. 2015-03-11. The $\aleph_{0}$-categorical Trees and Cycle-free Partial Orders. https://arxiv.org/abs/1503.03336

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