Date of Award
Master of Arts (MA)
Dr. J. Scott Downing
In this thesis axioms for set theory will be presented which include the well-known axiom of choice. These axioms, together with their associated primitives, defined terms, and theorems will be referred to as the BGN (for Bernays, Godel, and von Neumann) theory or sets, or just BGN. BGN, without the axiom of' choice and theorems requiring it, will be denoted by BGN 1. It will be shown that if a proposition attributing a property to countable sets can be proved in BGN, then it can be proved in BGN, by showing that the axiom of choice (Zermelo’s form) when stated for countable sets, is a theorem of BGN.
Mansfield, Roger L., "The axiom of choice for countable sets." (1972). Student Work. 3548.