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We show that a product subsystem of a time ordered system (that is, a productsystem of time ordered Fock modules), though type I, need not be isomorphic toa time ordered product system. In that way, we answer an open problem in theclassification of CP-semigroups by product systems. We define spatial stronglycontinuous CP-semigroups on a unital C*-algebra and characterize them as thosethat have a Christensen-Evans generator.

Subsystems of Fock Need Not Be Fock: Spatial CP-Semigroups