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Preprint Number 971

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971. Tapani Hyttinen and Gianluca Paolini
Beyond AECs: On Model Theory of Geometric Lattices

Submission date: 4 December 2015


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

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Full text arXiv 1512.01457: pdf, ps.

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