Generic stability, regularity, and quasiminimality

Anand Pillay; Predrag Tanovic

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arXiv · 0912.1115

Generic stability, regularity, and quasiminimality

Anand Pillay·Predrag Tanovic

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Abstract

We study the notions generic stability, regularity, homogeneous pregeometries, quasiminimality, and their mutual relations, in an arbitrary first order theory T. We prove that "infinite-dimensional homogeneous pregeometries" coincide with generically stable strongly regular types (p(x),x=x). We prove that quasiminimal structures of cardinality at least aleph-2 are homogeneous pregeometries, We prove that the generic type of an arbitrary quasiminimal structure is locally strongly regular. Some of the results depend on a general dichotomy for regular-like types: generic stability, or existence of a suitable definable partial ordering.

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BibTeX RIS

Anand Pillay, Predrag Tanovic. 2009-12-06. Generic stability, regularity, and quasiminimality. https://arxiv.org/abs/0912.1115

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