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Gödel's incompleteness theorem

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems)

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