The ℵ₀-categorical Trees and Cycle-free Partial Orders

2015/03/11 by Barham, Robert
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1503.03336

Abstract

We provide a description of the structure of ℵ₀-categorical trees and cycle-free partial orders. First the maximal branches of ℵ₀-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 ℵ₀-categorical in terms of these two things. The classification of the ℵ₀-categorical cycle-free partial orders is found as a corollary.

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• Reconstruction of non-ℵ₀-categorical theories