Submission date: 6 July 2021

Abstract:

We study finitely homogeneous dependent rosy structures, adapting results of Cherlin, Harrington, and Lachlan proved for ω-stable ω-categorical structures. In particular, we prove that such structures have finite þ-rank and are coordinatized by a þ-rank 1 set. We show that they admit a distal, finitely axiomatizable, expansion.
These results show that there are, up to inter-definability, at most countably many dependent rosy structures M which are homogeneous in a finite relational language.

Mathematics Subject Classification: 03C45

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Full text arXiv 2107.02727: pdf, ps.