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Recursive functions and decidability Godefs exact theorem Undecidability of truth
and theorem- hood Proof independent of set theory Turing's undecid- ability proof
Range. In particular, he discovered that if such a system is a>-consistent ...
Godel's original proof of the completeness theorem is closely related to the
second proof above. Consideration may again ... Mm — are not satisfiable; i.e.,
their negations are tautologies (theorems of the propositional calculus). Thus, ~M
,j V ..
The part of Godel's theorem that —A, is unprovable but true shows that not even
the first step can be carried out fully. Despite the value of the logistic method as a
way of defining exactly the presuppositions of a given portion of mathematics, ...
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