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On some definitions of a finite set Gutteridge, Lance
Abstract
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.
Item Metadata
Title |
On some definitions of a finite set
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1969
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Description |
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.
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-05-20
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Provider |
Vancouver : University of British Columbia Library
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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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DOI |
10.14288/1.0080467
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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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.