Amalgamation in Finite Dimensional Cylindric Algebras
Maarten Marx

For every finite n>1, the embedding property fails in the class of
all n-dimensional cylindric type algebras which  satisfy the
following. Their boolean reducts are boolean algebras and two of the
cylindrifications are normal, additive and commute.
This result also holds for    all   subclasses containing the
representable n-dimensional cylindric algebras. This considerably
strengthens a result of S.~Comer on CAn and provides a
strong counterexample for interpolation in finite variable fragments
of first order logic.
We provide a new modern proof, using an  argument inspired by modal logic.

Mathematics Subject Classification: 03G15, 03C40. 
Keywords: cylindric algebras, amalgamation, interpolation.