Algebraic geometry over Boolean algebras in the language with constants

Abstract: 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.