A finitely axiomatizable undecidable equational theory with recursively solvable word problems

In this paper we construct a finitely based variety, whose equational theory is undecidable, yet whose word problems are recursively solvable, which solves a problem stated by G. McNulty (1992). The construction produces a discriminator variety with the aforementioned properties starting from a class of structures in some multisorted language (which may include relations), axiomatized by a finite set of universal sentences in the given multisorted signature. This result also presents a common generalization of the earlier results obtained by B. Wells (1982) and A. Mekler, E. Nelson, and S. Shelah (1993).