Datensatz

Zusammenfassung

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 logics 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 holds, but also under what extensions, both to the language and proof system, it remains valid. We show that FS/sub 0/, a system for formal metamathematics, provides a basis for organizing theories this way, and we report on our practical experience.