Infinitary propositional relevant languages with absurdity

Guillermo Badia

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arXiv · 1809.08153

Infinitary propositional relevant languages with absurdity

Guillermo Badia

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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 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.

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Guillermo Badia. 2018-09-21. Infinitary propositional relevant languages with absurdity. https://arxiv.org/abs/1809.08153

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