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We study what we call topological cylindric algebras and tense cylindricalgebras defined for every ordinal $\alpha$. The former are cylindric algebrasof dimension $\alpha$ expanded with $\sf S4$ modalities indexed by $\alpha$.The semantics of representable topological algebras is induced by the interioroperation relative to a topology defined on their bases. Tense cylindricalgebras are cylindric algebras expanded by the modalities $F$(future) and $P$(past) algebraising predicate temporal logic.  We show for both tense and topological cylindric algebras of finite dimension$n>2$ that infinitely many varieties containing and including the variety ofrepresentable algebras of dimension $n$ are not atom canonical. We show thatany class containing the class of completely representable algebras having aweak neat embedding property is not elementary. From these two results we drawthe same conclusion on omitting types for finite variable fragments ofpredicate topologic and temporal logic. We show that the usual version of theomitting types theorem restricted to such fragments when the number ofvariables is $>2$ fails dramatically even if we considerably broaden the classof models permitted to omit a single non principal type in countable atomictheories, namely, the non-principal type consting of co atoms.

Algebraic analysis of temporal and topological finite variable fragments, using cylindric modal algebras