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Gödel's Incompleteness Theorems

[Revised entry by Panu Raatikainen on January 20, 2015. Changes to: Main text, sup2.html] Godel's two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the limits of provability in formal axiomatic theories. The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F....
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