We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. We give several examples, including a homotopy theory for G-spaces, where G is a profinite group. The class of weak equivalences are an approximation to the class of underlying weak equivalences.
Homology, Homotopy and Applications, Vol. 9 (2007), No. 1, pp.367-398.