Amalgamation in finite dimensional cylindric algebras (Q1866797)

Let \(\alpha \) be an ordinal. Let \(CA_{\alpha }, RCA_{\alpha }, NCA_{\alpha } \) denote the classes of all \(\alpha \)-dimensional cylindric algebras, representable cylindric algebras and noncommutative cylindric algebras, respectively. It was shown by S. Comer that for finite \(n>1\), the embedding property fails in any class between \(RCA_n \) and \(CA_n\). On the other hand, I. Neméti proved that for any \(\alpha \) the class \(NCA_{\alpha }\) has the strong amalgamation property. The author presents a new proof of the last statement and describes large enough classes \(K_n\) of \(n\)-dimensional cylindric algebras satisfying certain conditions which fail to enjoy the embedding and/or amalgamation property.