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It is shown how consistent histories quantum cosmology can be realisedthrough Isham's Histories Projection Operator consistent histories scheme. Thisis done by using an affine algebra instead of a canonical one and also by usingcocycle representations. A regularisation scheme allows us to find a historyHamiltonian which exists as a proper self-adjoint operator. The role of acocycle choice is also discussed.Comment: 31 pages, LaTeX, no figure

Affine histories in quantum gravity: introduction and the representation for a cosmological model