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Unification in intuitionistic logic. (English) Zbl 0930.03009
Summary: We show that the variety of Heyting algebras has finitary unification type. We also show that the subvariety obtained by adding the De Morgan law is the biggest variety of Heyting algebras having unitary unification type. Proofs make essential use of suitable characterizations (both from the semantic and the syntactic side) of finitely presented projective algebras.

MSC:
03B35 Mechanization of proofs and logical operations
03B20 Subsystems of classical logic (including intuitionistic logic)
06D20 Heyting algebras (lattice-theoretic aspects)
08B30 Injectives, projectives
03B55 Intermediate logics
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