TY - THES
AU - Gutteridge, Lance
PY - 1969
TI - On some definitions of a finite set
KW - Thesis/Dissertation
LA - eng
M3 - Text
AB - 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.
N2 - 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.
UR - https://open.library.ubc.ca/collections/831/items/1.0080467
ER - End of Reference