Intersection of noncharacterizable varieties of lattices (Q810068)

A variety V is said to be characterizable by a set M of finite lattices, and the lattices themselves prohibited for V (for the sake of brevity, such varieties will be called simply characterizable), if V coincides with the class of all lattices in which no lattice from M can be embedded. The author [Algebra Logika 27, No.3, 305-315 (1988; Zbl 0666.06004)] has constructed examples of noncharacterizable varieties of lattices. In connection with this, D. M. Smirnov has posed the question of the existence of noncharacterizable varieties, whose intersection is characterizable. In this paper we answer this question affirmatively.