Date of Award

2011

Document Type

Thesis

Degree Name

Master of Science (MS) in Mathematics

Department

Mathematics

First Advisor

Dale Garraway

Second Advisor

Yves Nievergelt

Third Advisor

Elizabeth Peterson

Abstract

"Incompleteness or inconsistency? Kurt Godel shocked the mathematical community in 1931 when he proved any effectively generated, sufficiently complex, and sound axiomatic system could not be both consistent and complete. This thesis will explore two formal languages of logic and their associated mechanically recursive proof methods with the goal of proving Godel's Incompleteness Theorems. This, in combination with an assignment of a natural number to every string of an axiomatic system, will be used to show a consistent system contains a true statement of the form "This sentence is unprovable," and a complete system contains a proof of its own consistency only if it is inconsistent"--Document.

Comments

Typescript. Vita.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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