Defense Date

2010

Document Type

Thesis

Degree Name

Master of Science

Department

Mathematical Sciences

First Advisor

Andrew Lewis

Abstract

We will discuss the 9th axiom of Zermelo-Fraenkel set theory with choice, which is often abbreviated ZFC, since it includes the axiom of choice (AC). AC is a controversial axiom that is mathematically equivalent to many well known theorems and has an interesting history in set theory. This thesis is a combination of discussion of the history of the axiom and the reasoning behind why the axiom is controversial. This entails several proofs of theorems that establish the fact that AC is equivalent to such theorems and notions as Tychonoff's Theorem, Zorn's Lemma, the Well-Ordering Theorem, and many more.

Rights

© The Author

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

May 2010

Share

COinS