On generalizations of a theorem of Vaught (Q2641299)

The abstract reads as follows: ``This paper deals with the cylindric algebraic version of Vaught's theorem on the existence of prime models of atomic theories. It is proved that the algebraic version proved by Serény, which states that under certain conditions every isomorphism between two cylindric set algebras (Cs's) is a lower base-isomorphism, extends the generalized cylindrical algebras (Gs's) although it does not extend to generalized weak cylindric set algebras (Gws's); indeed, it is not true for weak cylindric set algebras (Ws's).''