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Gödel's incompleteness theorems
Gödel's incompleteness theorems
are two
theorems
of
mathematical logic
that establish inherent limitations of all but the most trivial
axiomatic systems
capable of doing
arithmetic
. The theorems, proven by
Kurt Gödel
in 1931, are important both in mathematical logic and in the
philosophy of mathematics
. The two results 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, giving a negative answer to
Hilbert's second problem
.
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