  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.
