Abstract
Publisher Summary This chapter discusses several metalogical notions referring to equational theories of algebras and, more generally, to equational logic. It also presents a short survey of the results obtained from these theories and open problems concerning these notions. The chapter also presents several decision problems. These problems are associated with the recursive nature of a given set of equations, or of finite sets of equations, or of finite algebras. The conceptually simplest decision problems concern the decidability of individual theories. A theory is called decidable simply if it is recursive. Most familiar equational theories and the theory of any finite algebra prove to be decidable. Further, as in the predicate logic, every complete theory with a finite (or, more generally, a recursive) base is decidable.
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