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INFINITARY PROPOSITIONAL RELEVANT LANGUAGES WITH ABSURDITY

Published online by Cambridge University Press:  01 August 2017

GUILLERMO BADIA
GUILLERMO BADIA*
Affiliation:
Department of Knowledge-Based Mathematical Systems Johannes Kepler Universität Linz
*
*DEPARTMENT OF KNOWLEDGE-BASED MATHEMATICAL SYSTEMS JOHANNES KEPLER UNIVERSITÄT LINZ LINZ, AUSTRIA E-mail: [email protected]
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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∞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.

Keywords

03B4703C75relevant logicmodel theoryinfinitary logicinterpolationRoutley–Meyer semantics
Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 4 , December 2017 , pp. 663 - 681
Copyright
Copyright © Association for Symbolic Logic 2017 

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