DOI
https://doi.org/10.25772/4Q6G-E655
Defense Date
2010
Document Type
Thesis
Degree Name
Master of Science
Department
Mathematical Sciences
First Advisor
Andrew Lewis
Abstract
Working within the Zermelo-Frankel Axioms of set theory, we will introduce two important contradictory axioms: Axiom of Choice and Axiom of Determinacy. We will explore perfect polish spaces and games on these spaces to see that the Axiom of Determinacy is inconsistent with the Axiom of Choice. We will see some of the major consequences of accepting the Axiom of Determinacy and how some of these results change when accepting the Axiom of Choice. We will consider 2-player games of perfect information wherein we will see some powerful results having to do with properties of the real numbers. We will use a game to illustrate a weak proof of the continuum hypothesis.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
May 2010