Date of Award

2012

Degree Name

Mathematics

College

College of Science

Type of Degree

M.A.

Document Type

Thesis

First Advisor

Carl Mummert

Second Advisor

John Drost

Third Advisor

Michael Schroeder

Abstract

The goal of reverse mathematics is to study the implication and non-implication relationships between theorems. These relationships have their own internal logic, allowing some implications and non-implications to be derived directly from others. The goal of this thesis is to characterize this logic in order to capture the relationships between specific mathematical works. The results of our study are a finite set of rules for this logic and the corresponding soundness and completeness theorems. We also compare our logic with modal logic and strict implication logic. In addition, we explain two applications of S-logic in topology and second order arithmetic.

Subject(s)

Reverse mathematics.

Logic - Mathematics.

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