| Consequence of
Goedels theorem |
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| n | Showed
we can not prove completeness of a |
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| consistent
set of arithmetic axioms. There will |
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| be
true statements that can not be proven. |
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| n | If
there existed a general procedure to derive |
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| the
minimal Turing machine program for any |
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| sequence,
then we would have a procedure to |
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| derive
any true proposition from a smaller set |
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| of
axioms, contra Goedel. |
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