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Bases of admissible rules of the logics S4 and Int. (English. Russian original) Zbl 0598.03014
Algebra Logic 24, 55-68 (1985); translation from Algebra Logika 24, No. 1, 87-107 (1985).
This paper uses results and notions of the author’s paper reviewed above (Zbl 0598.03013) to prove for intuitionistic propositional calculus Int and for S4 that the set of admissible rules does not possess a finite basis. In fact even an infinite basis containing a finite set of variables is proved to be impossible.
Reviewer: G.E.Mints

MSC:
03B45 Modal logic (including the logic of norms)
03F50 Metamathematics of constructive systems
03B25 Decidability of theories and sets of sentences
03B55 Intermediate logics
03B60 Other nonclassical logic
03G25 Other algebras related to logic
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References:
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