Madarász, J. X. and Németi, I.

Free Boolean algebras with closure operators and a conjecture of Henkin, Monk, and Tarski

We characterize the finite-dimensional elements of a free cylindric algebra. This solves Problem 2.10 in [Henkin, Monk, Tarski: Cylindric Algebras, North-Holland, 1971 and 1985]. We generalize the characterization to quasi-varieties of Boolean algebras with operators in place of cylindric algebras.