Applications of De Morgan toposes and the Gleason cover
In intuitionistic propositional logic, one of the so-called De Morgan's laws is not valid. This thesis studies the non intuitionistically valid one, namely, $ neg( phi wedge psi)= neg phi vee neg psi$, (denoted by (DML)), with examples and applications in topology, algebra, analysis, logic and...
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McGill University
1996
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ftcanadathes:oai:collectionscanada.gc.ca:QMM.27336 2023-05-15T16:01:21+02:00 Applications of De Morgan toposes and the Gleason cover Harun, Rona. Bunge, Marta (advisor) Master of Science (Department of Mathematics and Statistics.) 1996 application/pdf http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=27336 en eng McGill University alephsysno: 001554235 proquestno: MQ29711 Theses scanned by UMI/ProQuest. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=27336 All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. Mathematics Electronic Thesis or Dissertation 1996 ftcanadathes 2014-02-16T00:47:26Z In intuitionistic propositional logic, one of the so-called De Morgan's laws is not valid. This thesis studies the non intuitionistically valid one, namely, $ neg( phi wedge psi)= neg phi vee neg psi$, (denoted by (DML)), with examples and applications in topology, algebra, analysis, logic and topos theory. In particular, we recall the Gleason cover of a topos which is a universal construction of a De Morgan topos covering the given one. This construction is then used in connection with the Hahn-Banach theorem in any topos of sheaves on a locale, and in order to obtain the real closure of an ordered field in any topos of sheaves on a Boolean space. We also show that an algebraic analogue of (DML) may be related to the Zariski spectrum of a ring. Finally, we examine (DML) in the contexts of model theory and locale theory. Thesis DML Theses Canada/Thèses Canada (Library and Archives Canada) Psi ENVELOPE(-63.000,-63.000,-64.300,-64.300) |
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Theses Canada/Thèses Canada (Library and Archives Canada) |
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language |
English |
topic |
Mathematics |
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Mathematics Harun, Rona. Applications of De Morgan toposes and the Gleason cover |
topic_facet |
Mathematics |
description |
In intuitionistic propositional logic, one of the so-called De Morgan's laws is not valid. This thesis studies the non intuitionistically valid one, namely, $ neg( phi wedge psi)= neg phi vee neg psi$, (denoted by (DML)), with examples and applications in topology, algebra, analysis, logic and topos theory. In particular, we recall the Gleason cover of a topos which is a universal construction of a De Morgan topos covering the given one. This construction is then used in connection with the Hahn-Banach theorem in any topos of sheaves on a locale, and in order to obtain the real closure of an ordered field in any topos of sheaves on a Boolean space. We also show that an algebraic analogue of (DML) may be related to the Zariski spectrum of a ring. Finally, we examine (DML) in the contexts of model theory and locale theory. |
author2 |
Bunge, Marta (advisor) |
format |
Thesis |
author |
Harun, Rona. |
author_facet |
Harun, Rona. |
author_sort |
Harun, Rona. |
title |
Applications of De Morgan toposes and the Gleason cover |
title_short |
Applications of De Morgan toposes and the Gleason cover |
title_full |
Applications of De Morgan toposes and the Gleason cover |
title_fullStr |
Applications of De Morgan toposes and the Gleason cover |
title_full_unstemmed |
Applications of De Morgan toposes and the Gleason cover |
title_sort |
applications of de morgan toposes and the gleason cover |
publisher |
McGill University |
publishDate |
1996 |
url |
http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=27336 |
op_coverage |
Master of Science (Department of Mathematics and Statistics.) |
long_lat |
ENVELOPE(-63.000,-63.000,-64.300,-64.300) |
geographic |
Psi |
geographic_facet |
Psi |
genre |
DML |
genre_facet |
DML |
op_relation |
alephsysno: 001554235 proquestno: MQ29711 Theses scanned by UMI/ProQuest. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=27336 |
op_rights |
All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
_version_ |
1766397255052427264 |