Positive model structures for abstract symmetric spectra

We give a general method of constructing positive stable model structures for symmetric spectra over an abstract simplicial symmetric monoidal model category. The method is based on systematic localization, in Hirschhorns sense, of a ceratin positive projective model structure on spectra, where positivity basically means the truncation of the zero slice. The localization above is by the set of stabilizing morphisms, or their truncated version.