  We define a general notion of partially ordered Jordan algebra (over a
partially ordered ring), and we show that the Jordan geometry associated to
such a Jordan algebra admits a natural invariant partial cyclic order, whose
intervals are modelled on the symmetric cone of the Jordan algebra. We define
and describe, by affine images of intervals, the interval topology on the
Jordan geometry, and we outline a reserch program aiming at generalizing main
features of the theory of classical symmetric cones and bounded symmetric
domains.
