  In the the present contribution, we prove an Omitting Types Theorem (OTT) for
an arbitrary fragment of hybriddynamic first-order logic with rigid symbols
(i.e. symbols with fixed interpretations across worlds) closed under negation
and retrieve. The logical framework can be regarded as a parameter and it is
instantiated by some well-known hybrid and/or dynamic logics from the
literature. We develop a forcing technique and then we study a forcing property
based on local satisfiability, which lead to a refined proof of the OTT. For
uncountable signatures, the result requires compactness, while for countable
signatures, compactness is not necessary. We apply the OTT to obtain upwards
and downwards L\"owenheim-Skolem theorems for our logic, as well as a
completeness theorem for its constructor-based variant. The main result of this
paper can easily be recast in the institutional model theory framework, giving
it a higher level of generality.
