EPSILON THEOREMS IN INTERMEDIATE LOGICS

Any intermediate propositional logic (i.e., a including intuitionistic and contained in classical logic) can be extended to calculus with epsilon- tau-operators critical formulas. For logic, this results Hilbert’s -calculus. The first second -theorems for establish conservativity of the -calculus over its base logic. It is well known that -theorem fails -calculus, as prenexation impossible. paper investigates effect adding - -formulas using translation quantifiers into -terms logics. shown also holds such -calculi. “extended” if finite-valued Gödel–Dummett otherwise, but certain provable formulas infinite-valued Gödel first-order methods used prove suggest applications theories arithmetic.