Six definitions of a finite set are studied; and each implication between the definitions is shown to be either derivable from the Zermelo-Fraenkel axioms or independent
of them. The method of Boolean-valued models, as studied by D. Scott, is used to show that it is consistent with the Zermelo-Fraenkel axioms to deny some of these implications by constructing appropriate models.
The six definitions are shown to satisfy a list of properties which a definition of finite should reasonably possess. It is also shown that any definition which satisfies these properties must encompass a larger class of sets than the first definition and a smaller class than the sixth.
Three more definitions, which do not possess these properties, are mentioned, and the differences between these definitions and the first six are discussed. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/34751 |
| Date | January 1969 |
| Creators | Gutteridge, Lance |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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