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dc.contributor.authorDyckhoff, Roy
dc.contributor.authorNegri, Sara
dc.identifier.citationDyckhoff , R & Negri , S 2015 , ' Geometrisation of first-order logic ' Bulletin of Symbolic Logic , vol. 21 , no. 2 , pp. 123–163 . DOI: 10.1017/bsl.2015.7en
dc.identifier.otherPURE: 181704500
dc.identifier.otherPURE UUID: dbf76454-5fcd-4d56-8269-69f62f7dcd21
dc.identifier.otherScopus: 84962091019
dc.description.abstractThat every first-order theory has a coherent conservative extension is regarded by some as obvious, even trivial, and by others as not at all obvious, but instead remarkable and valuable; the result is in any case neither sufficiently well-known nor easily found in the literature. Various approaches to the result are presented and discussed in detail, including one inspired by a problem in the proof theory of intermediate logics that led us to the proof of the present paper. It can be seen as a modification of Skolem’s argument from 1920 for his “Normal Form” theorem. “Geometric” being the infinitary version of “coherent”, it is further shown that every infinitary first-order theory, suitably restricted, has a geometric conservative extension, hence the title. The results are applied to simplify methods used in reasoning in and about modal and intermediate logics. We include also a new algorithm to generate special coherent implications from an axiom, designed to preserve the structure of formulae with relatively little use of normal forms.en
dc.relation.ispartofBulletin of Symbolic Logicen
dc.rightsCopyright © The Association for Symbolic Logic 2015. Originally published in The Bulletin of Symbolic Logic. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectCoherent implicationen
dc.subjectCoherent logicen
dc.subjectGeometric logicen
dc.subjectWeakly positive formulaen
dc.subjectQA75 Electronic computers. Computer scienceen
dc.subjectQA Mathematicsen
dc.titleGeometrisation of first-order logicen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. School of Computer Scienceen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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