Hypervarieties of a given type (Q751684)

The paper concerns the notions of hyperidentities and hypervarieties. In particular solid varieties are defined and studied. An algebra A is solid if every identity satisfied in \({\mathfrak A}\) is transformed into a hyperidentity which is satisfied in \({\mathfrak A}\) (i.e. it is satisfied in the variety generated by \({\mathfrak A})\). The authors study the logic connected with hyperidentities and prove a completeness theorem which combines this logic with solid varieties. Further a slight reformulation of Birkhoff's completeness theorem for identities is proved.