DOI
https://doi.org/10.25772/5D1H-QX40
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