  We study what we call topological cylindric algebras and tense cylindric
algebras defined for every ordinal $\alpha$. The former are cylindric algebras
of dimension $\alpha$ expanded with $\sf S4$ modalities indexed by $\alpha$.
The semantics of representable topological algebras is induced by the interior
operation relative to a topology defined on their bases. Tense cylindric
algebras 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 of
representable algebras of dimension $n$ are not atom canonical. We show that
any class containing the class of completely representable algebras having a
weak neat embedding property is not elementary. From these two results we draw
the same conclusion on omitting types for finite variable fragments of
predicate topologic and temporal logic. We show that the usual version of the
omitting types theorem restricted to such fragments when the number of
variables is $>2$ fails dramatically even if we considerably broaden the class
of models permitted to omit a single non principal type in countable atomic
theories, namely, the non-principal type consting of co atoms.
