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Computability theory a.k.a. recursion theory.

28 votes
4 answers
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Church's Theorem and Gödel's Incompleteness Theorems

I have recently been reading up on some of the ideas and history of the ground-breaking work done by various logicians and mathematicians regarding computability. … Finally, can we essential say that the concept of provability in a formal system (proof calculus) is identical to the concept of computability in recursion theory (Turing machines/lambda calculus)? …
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