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On structurally complete superintuitionistic logics. (English. Russian original) Zbl 0412.03009
Sov. Math., Dokl. 19, 816-819 (1978); translation from Dokl. Akad. Nauk SSSR 241, 40-43 (1978).
Summary: The author uses algebraic methods to study questions of structural completeness for superintuitionistic logics. Among the main results is the following (Theorem 4): a necessary and sufficient condition for a superintuitionistic logic to be hereditarily structurally complete is that it not be included in Dummett’s logic LC nor in any one of five logics specified by the author by means of small finite algebras.
Reviewer’s comments: The reader may find it useful to compare some of the author’s work with other independently obtained results. In particular, although the methods of proof are different, Theorem 1 is clearly related to the main result of Z. Dywan’s “Decidability of structural completeness for strongly finite propositional calculi” [Bull. Sect. Logic, Pol. Acad. Sci. 7, 129–132 (1978; Zbl 0408.03018)]; and the author’s lemma 1 has interesting connections with Theorems 1 and 2 of T. Prucnal’s and A. Wroński’s abstract “An algebraic characterization of the notion of structural completeness” [ibid. 3, 30–33 (1974); http://www.filozof.uni.lodz.pl/bulletin/pdf/03_1_9.pdf].
Reviewer: D. Makinson

MSC:
03B55 Intermediate logics
03B99 General logic
03G10 Logical aspects of lattices and related structures
06D15 Pseudocomplemented lattices
06D20 Heyting algebras (lattice-theoretic aspects)
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