The structure of saturated free algebras

Requiring an algebra M to be both free (for the variety it generates) and א₁-saturated imposes very strong conditions on M. In the simplest examples (see below) there exist a finite number of relatively free algebras A_o,..., A_n-1 whose theories are א₁-categorical such that M is generated (as an algebra) by the U A_i In particular, this implies Th(M) has at most (α+א_o) models of cardinality א_α. We will show a weaker structure theorem in the general case but deduce the same constraint on the spectrum of T.