  Analogues of Scott's isomorphism theorem, Karp's theorem as well as results
on lack of compactness and strong completeness are established for infinitary
propositional relevant logics. An "interpolation theorem" (of a particular sort
introduced by Barwise and van Benthem) for the infinitary quantificational
boolean logic $L_{\infty \omega}$ holds. This yields a preservation result
characterizing the expressive power of infinitary relevant languages with
absurdity using the model-theoretic relation of relevant directed bisimulation
as well as a Beth definability property.
