Applications of De Morgan toposes and the Gleason cover

• Main Author: Harun, Rona.
• Other Authors: Bunge, Marta (advisor)
• Format: Thesis
• Language: English
• Published: McGill University 1996
• Subjects: Mathematics; Psi; DML
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=27336

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.