Date of Award


Document Type


Degree Name

Master of Arts (MA)



First Advisor

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.


A Thesis Presented to the Department of Mathematics and the Faculty of the Graduate College University of Nebraska In Partial Fulfillment of the Requirements for the Degree Master of Arts University of Nebraska at Omaha. Copyright 1972 Roger L. Mansfield