Introduces rgs and irgs for Keisler measures with characterizations via formula averages, shows coincidence with fim for types, proves irgs implies dependence and symmetry, and zero measure for instability events O^φ, I^φ, L^φ.
Generic stability, regularity, and quasiminimality
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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.
fields
math.LO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Keisler Measures and Generically Stable Random Types
Introduces rgs and irgs for Keisler measures with characterizations via formula averages, shows coincidence with fim for types, proves irgs implies dependence and symmetry, and zero measure for instability events O^φ, I^φ, L^φ.