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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 ω 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.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
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