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Hyperidentities of De Morgan algebras. (English) Zbl 1276.06005

The authors introduce the concept of canonical hyperidentities for words in the language of De Morgan algebras. It is proved that every hyperidentity is equivalent in the variety of De Morgan algebras to a canonical hyperidenty, and that this canonical hyperidentity can be obtained by a finite number of syntactic transformations. This is later used to present an axiomatisation of the hyperequational theory of De Morgan algebras and to prove that this theory is decidable.

MSC:

06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
03B25 Decidability of theories and sets of sentences
03C05 Equational classes, universal algebra in model theory
08B15 Lattices of varieties
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