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Generic stability, regularity, and quasiminimality

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arxiv 0912.1115 v2 pith:43WFHJQQ submitted 2009-12-06 math.LO

Anand Pillay , Predrag Tanovic This is my paper · ORCID
classification math.LO
keywords generichomogeneouspregeometriesprovestabilityarbitraryquasiminimalquasiminimality
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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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Cited by 1 Pith paper

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  1. Keisler Measures and Generically Stable Random Types

    math.LO 2026-05 unverdicted novelty 6.0 of 10

    Introduces rgs and irgs for Keisler measures with equivalences to generic stability of random types and proves irgs implies dependence.

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