Varieties and quasivarieties of algebras are classes of algebras which can be defined by means of a collection of identities and quasi-identities (conditional identities), respectively. Since identities and quasi-identities are ∀-formulas, varieties and quasivarieties are particular types of universally axiomatizable classes of algebras whose general properties were studied in Section 7. The special position of quasivarieties and especially varieties in general algebra is due to the fact that many structures intensely investigated in classical algebra such as groups, rings, lattices, Boolean algebras, etc., form varieties.
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