Varieties with decidable finite algebras II: Permutability

This paper is a continuation of 3]. Congruence permutability is shown to be a necessary condition for a locally finite congruence distributive variety to have a decidable first order theory of its finite algebras. This is a positive answer to Problem 6 of S. Burns and H. P. Sankappanavar 2]. Moreover this allows us to give a full characterization of finitely generated congruence distributive varieties of finite type with decidable first order theories of their finite members.Presented by Stanley Burris.