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Preprint Number 217
217. Anand Pillay and Predrag Tanovic
Generic stability, regularity, and quasiminimality
Submission date: 6 December 2009.
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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