Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 217

Preprint Number 217

Previous Next Preprint server

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

Keywords and phrases:

Full text arXiv: pdf, ps.

Last updated: March 23 2021 09:21 Please send your corrections to: