On reproductive solutions of Postian and Stonean equations

Abstract

A theorem due to L¨owenheim provides the general reproductive solution of a Boolean equation whenever a particular solution is known. This theorem has been generalized either by passing from Boolean algebras to Post algebras and Stone algebras, by using a parametric solution instead of a particular solution or by combining the two directions. In the present paper, we survey this research and generalize everything to Stone algebras.