The axiom of choice for countable sets.

Author

Roger L. Mansfield

Date of Award

7-1-1972

Document Type

Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

First Advisor

Dr. J. Scott Downing

Abstract

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.

Comments

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

Recommended Citation

Mansfield, Roger L., "The axiom of choice for countable sets." (1972). Student Work. 3548.
https://digitalcommons.unomaha.edu/studentwork/3548