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A global existence theorem, with respect to a geometrically defined time, isshown for Gowdy symmetric globally hyperbolic solutions of the Einstein-Vlasovsystem for arbitrary (in size) initial data. The spacetimes being studiedcontain both matter and gravitational waves.Comment: Latex, 40 pages, submitted to CM

Global Foliations of Matter Spacetimes¶with Gowdy Symmetry