# Tagged Questions

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### History of provably total functions of a theory

Provably total functions of an arithmetical theory is one of the tools used in proof theoretic analysis of theories.
I am looking for early history of its development. In particular,
Where was ...

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### “Let $x \in A$”, beginning a proof of “$\forall x \in A$ …”, if A were empty [closed]

I work at a four-year teaching school, where we pride ourselves on teaching pure math, proof, and a rather obsessive carefulness of work. Recently I have been criticized for saying that "Let $x \in ...

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### What was Gödel's real achievement?

When I first heard of the existence of Gödel's theorem, I was amazed not just at the theorem but at the fact that the question could be made precise enough to answer: how on earth, even in ...