VARIETIES GENERATED BY QUASI-PRIMAL ALGEBRAS HAVE DECIDABLE THEORIES

Abstract

This chapter examines the varieties generated by quasi-primal algebras have decidable theories. A finite algebra P that does only depend on u and not on the sheaf or its base space such that the sheaf started with can be embedded as a subsheaf in the constant sheaf with stalks P and the same base space. The sheaf-representations are considered provided the represented algebra is countable. Applying the techniques and using Comer's decidability result, the decidability of the theories of all varieties that are generated by a weakly independent set of quasi-primal algebras is established. The chapter presents some known examples of decidable theories that appear as special cases and some new decidable theories such as infinitely many varieties of cylindric algebras with decidable theories.