Submission date: 6 December 2009.

Abstract:

We study the notions of generic stability, regularity, homogeneous pregeometries, quasiminimality, and their mutual relations, in arbitrary first order theories. We prove that “infinite-dimensional homo- geneous pregeometries” coincide with generically stable strongly regular types (p(x), x = x). We prove that in a theory without the strict order property, regular types are generically stable, and prove analogous results for quasiminimal structures. We prove that the “generic type” of a quasiminimal structure is “locally strongly regular”.

Mathematics Subject Classification: 03C45

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