Saturated free algebras revisited

Abstract

We give an exposition of results of Baldwin-Shelah on saturated free algebras, at the level of generality of complete first order theories $T$ with a saturated model $M$ which is in the algebraic closure of an indiscernible set. We then make some new observations when $M$ is a saturated free algebra, analogous to (more difficult) results for the free group, such as a description of forking.