College - Author 1
College of Science and Mathematics
Department - Author 1
Mathematics Department
Degree Name - Author 1
BS in Mathematics
Date
12-2010
Primary Advisor
Todor Todorov
Abstract/Summary
The main goal of this project is to prove the equivalency of several characterizations of completeness of Archimedean ordered fields; some of which appear in most modern literature as theorems following from the Dedekind completeness of the real numbers, while a couple are not as well known and have to do with other areas of mathematics, such as nonstandard analysis. Continuing, we study the completeness of non-Archimedean fields, and provide several examples of such fields with varying degrees of properties, using nonstandard analysis to produce some relatively "nice" (in particular, they are Cantor complete) final examples. As a small detour, we present a short construction of the real numbers using methods from nonstandard analysis.
URL: https://digitalcommons.calpoly.edu/mathsp/3