  We study equations over boolean algebras with distinguished elements. We
prove the criteria, when a boolean algebra is equationally Noetherian, weakly
equationally Noetherian, $\mathbf{q}_\omega$-compact or
$\mathbf{u}_\omega$-compact. Also we solve the problem of geometric equivalence
in the class of boolean algebras with distinguished elements.

Rings and Algebras