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Full-Text Articles in Physical Sciences and Mathematics
GöDel's Incompleteness Theorem, Christopher Mullins
GöDel's Incompleteness Theorem, Christopher Mullins
EWU Masters Thesis Collection
"This thesis gives a rigorous development of sentential logic and first-order logic as mathematical models of humanity's deductive thought processes. Important properties of each of these models are stated and proved including Compactness results (the ability to prove a statement from a finite set of assumptions), Soundness results (a proof given a set of assumptions will always be true given that set of assumptions), and Completeness results (a statement that is true given a set of assumptions must have a proof from that set of assumptions). Mathematical theories and axiomatizations or theories are discussed in a first- order logical setting. …
Godel's Incompleteness Theorems, Jessica Dickson
Godel's Incompleteness Theorems, Jessica Dickson
EWU Masters Thesis Collection
"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 …