  Based on Crapo's theory of one point extensions of combinatorial geometries,
we find various classes of geometric lattices that behave very well from the
point of view of stability theory. One of them, $(\mathbf{K}^3, \preccurlyeq)$,
is $\omega$-stable, it has a monster model and an independence calculus that
satisfies all the usual properties of non-forking. On the other hand, these
classes are rather unusual, e.g. in $(\mathbf{K}^3, \preccurlyeq)$ the
Smoothness Axiom fails, and so $(\mathbf{K}^3, \preccurlyeq)$ is not an
$\mathrm{AEC}$.
