In "Sheaf Theory and the Continuum Hypothesis", Lawvere and Tierney proved the consistency of the negation of the continuum hypothesis with the theory of Set-like toposes. In this thesis, I generalize the Lawvere-Tierney result in two directions. Lawvere and Tierney's result relies upon the law of excluded middle and the axiom of choice, and I provide a formulation and proof of the consistency of the negation of the continuum hypothesis which abandons this assumption. Moreover, I generalize the work that's been done on the continuum hypothesis and its consistency from the context of topos theory presented in the Lawvere-Tierney proof to the context of algebraic set theory. / Dans "Sheaf Theory and the Continuum Hypothesis", Lawvere et Tierney ont démontré la compatibilité de la négation de l'hypothèse du continu avec la théorie des topos qui ressemblent au Set. Dans cette thèse, j'universalise le résultat de Lawvere-Tierney dans deux directions. Le résultat de Lawvere-Tierney compte sur le principe du tiers exclu et l'axiome du choix, et je fournis une formulation et une démonstration de la consistance de la négation de l'hypothèse du continu qui abandonne cette assomption. Aussi, j'universalise tous ces résultats sur l'hypothèse du continu et sa consistance de la contexte de la théorie du topos à la contexte de la théorie algébrique des ensembles.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.32368 |
| Date | January 2009 |
| Creators | Kusalik, Timothy |
| Contributors | Michael Makkai (Internal/Supervisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Mathematics and Statistics) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | Electronically-submitted theses. |
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