Godel's incompleteness theorems

<p>"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.</p>

Name thesis:degree_name

Master of Science (MS) in Mathematics

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics

Year

2011

Author dc:creator

• Dickson, Jessica

Contributors dc:contributor

• Dale Garraway
• Yves Nievergelt
• Elizabeth Peterson

• Logic
• Symbolic and mathematical
• Gödel's theorem
• Proof theory
• Physical Sciences and Mathematics

Statement dc:rights

• Access is available to all users

Repository record dc:identifier

https://dc.ewu.edu/theses/3

OAI identifier oai:identifier

oai:dc.ewu.edu:theses-1002