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Incompleteness

Incompleteness. Suppose L is a logic and H(T,x) is a statement in L expressing that Turing machine T halts on input x. Thus H(T,x) is true if and only if T halts on input x. Recall -- L is sound and effective. So: If H(T,x) is provable in L then it is true so T halts on input x.

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Incompleteness