The Elementary Classes of Direct and Boolean Products

Abstract

We characterize the elementary classes generated from a distinguished subclass closing by taking direct products and elementary equivalence. In the second part we give the same characterization in terms of atomic Boolean products. In the last part, we study the cases when the class of Boolean products is elementary but is not given by a discriminator.Mathematics Subject Classification: 03C30, 08C10, 03C05, 03C60.