\"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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Dickson, Jessica"],"institution":null,"degree_name":"Master of Science (MS) in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Dale Garraway","Yves Nievergelt","Elizabeth Peterson"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-01T08:00:00Z","date_published":"2011-01-01T08:00:00Z","updated_at":"2026-07-24T02:12:52Z","subjects":["Logic","Symbolic and mathematical","Gödel's theorem","Proof theory","Physical Sciences and Mathematics"],"languages":[],"rights":["Access is available to all users"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.ewu.edu/theses/3","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dale Garraway","Yves Nievergelt","Elizabeth Peterson"]},{"key":"dc:creator","label":"Author","values":["Dickson, Jessica"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS) in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Logic","Symbolic and mathematical","Gödel's theorem","Proof theory","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Access is available to all users"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dc.ewu.edu/theses/3"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["\"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.
"]},{"key":"dc:title","label":"Title","values":["Godel's incompleteness theorems"]}]}],"canonical_facts":{"dc:contributor":["Dale Garraway","Yves Nievergelt","Elizabeth Peterson"],"dc:creator":["Dickson, Jessica"],"dc:description.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.
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