On some Kripke complete and Kripke incomplete intermediate predicate logics

Studia Logica 61 (2):281-292 (1998)
The Kripke-completeness and incompleteness of some intermediate predicate logics is established. In particular, we obtain a Kripke-incomplete logic (H* +A+D+K) where H* is the intuitionistic predicate calculus, A is a disjunction-free propositional formula, D = x(P(x) V Q) xP(x) V Q, K = ¬¬x(P(x) V ¬P(x)) (the negative answer to a question of T. Shimura).
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1023/A:1005029515564
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