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• W2958446234 abstract "By adding a $tau$ operator, versions of Hilbert's $varepsilon$-calculus can be obtained for intermediate propositional logics including intuitionistic logic. It is well known that such calculi, in contrast to the $varepsilon$-calculus for classical logic, are not conservative. In particular, any $varepsilon$-$tau$ calculus for an intermediate logic proves all classically valid quantifier shift principles. The resulting calculi are however conservative over their propositional fragments. One important result pertaining to the $varepsilon$-calculus is the first epsilon theorem, which is closely related to Herbrand's theorem for existential formulas. It is shown that finite-valued Godel logics have the first epsilon theorem, and no other intermediate logic does. However, there are partial results for other intermediate logics including Godel-Dummett logic, the logic of weak excluded middle, and intuitionistic logic." @default.
• W2958446234 created "2019-07-23" @default.
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• W2958446234 date "2019-07-10" @default.
• W2958446234 modified "2023-09-27" @default.
• W2958446234 title "The First Epsilon Theorem in Pure Intuitionistic and Intermediate Logics" @default.
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