Schuda, Deborah - The Axiom of Choice and Its Ramifications, Advisor Dr. Otero
The Axiom of Choice in its general description is not very surprising and, in fact, seems obvious. That is why many mathematicians have used it without any hesitation. It is only within the last century or so that the Axiom of Choice was given its name and given any special attention. While at first glance the axiom seems obvious, some of its ramifications can be quite surprising. The Banach-Tarski Paradox is one such surprise. We will be presenting some statements equivalent to the Axiom of Choice although their intuitive comprehension can vary widely. We will also be presenting a few surprising and not so surprising results that directly hinge on the Axiom of Choice.