INFINITARY PROPOSITIONAL RELEVANT LANGUAGES WITH ABSURDITY
Guillermo Badía · The Review of Symbolic Logic · 2017
Abstract 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 logicL∞ωholds. 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.