We examine a problem in formal metatheory: if theories are structured hierarchically, there are metatheorems which hold in only some extensions. We illustrate this using modal ligics and the deduction theorem. We show how statements of metatheorems in such hierarchies can take account of possible theory extensions; i.e. a metatheorem formalizes not only the theory in which it hold,s but also under what extensions, both to the language and proof system, t remains valid. We show that FS_0, a sytem for formal metamathematics, provides a basis for orgnaizing theories this way, and we report on our practical experience.
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