Files in this item
Geometrisation of first-order logic
Item metadata
dc.contributor.author | Dyckhoff, Roy | |
dc.contributor.author | Negri, Sara | |
dc.date.accessioned | 2015-06-12T12:10:01Z | |
dc.date.available | 2015-06-12T12:10:01Z | |
dc.date.issued | 2015-06 | |
dc.identifier.citation | Dyckhoff , R & Negri , S 2015 , ' Geometrisation of first-order logic ' , Bulletin of Symbolic Logic , vol. 21 , no. 2 , pp. 123–163 . https://doi.org/10.1017/bsl.2015.7 | en |
dc.identifier.issn | 1079-8986 | |
dc.identifier.other | PURE: 181704500 | |
dc.identifier.other | PURE UUID: dbf76454-5fcd-4d56-8269-69f62f7dcd21 | |
dc.identifier.other | Scopus: 84962091019 | |
dc.identifier.other | WOS: 000355799500002 | |
dc.identifier.uri | https://hdl.handle.net/10023/6818 | |
dc.description.abstract | That 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. | |
dc.format.extent | 41 | |
dc.language.iso | eng | |
dc.relation.ispartof | Bulletin of Symbolic Logic | en |
dc.rights | Copyright © 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 http://dx.doi.org/10.1017/bsl.2015.7 | en |
dc.subject | Coherent implication | en |
dc.subject | Coherent logic | en |
dc.subject | Geometric logic | en |
dc.subject | Weakly positive formula | en |
dc.subject | QA75 Electronic computers. Computer science | en |
dc.subject | QA Mathematics | en |
dc.subject | NDAS | en |
dc.subject.lcc | QA75 | en |
dc.subject.lcc | QA | en |
dc.title | Geometrisation of first-order logic | en |
dc.type | Journal article | en |
dc.description.version | Postprint | en |
dc.contributor.institution | University of St Andrews. School of Computer Science | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1017/bsl.2015.7 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | http://www.math.ucla.edu/~asl/bsltoc.htm | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.