Nonequational Stable Groups

Abstract

We introduce a combinatorial criterion for verifying whether a formula is not the conjunction of an equation and a co-equation. Using this, we give a proof for the nonequationality of the free group. Furthermore, we generalize the latter result to the first-order theory of any free product of groups of the form $G\ast {\mathbb{F}}_{\omega }$.

10 pages, version accepted in the Proc. Am. Math. Soc