Submission date: 4 December 2015

Abstract:

Based on Crapo's theory of one point extensions of combinatorial geometries, we find various classes of geometric lattices that behave very well from the point of view of stability theory. One of them, K^3, is ω-stable, it has a monster model and an independence calculus that satisfies all the usual properties of non-forking. On the other hand, these classes are rather unusual, e.g. the class K^3 is not an abstract elementary class, in fact the Smoothness Axiom fails.

Mathematics Subject Classification: 03C48, 03C45, 06B99, 05E99

Keywords and phrases:

Full text arXiv 1512.01457: pdf, ps.