Talk:Diagonalization lemma

The typeset judgement is not only wrong, but is not well-formed: the hole in phi(-) accepts only terms (that is, in arithmetic, arithmetic expressions).

It should read:

P |- psi <=> phi(#psi)

where #- is the Goedel numbering function.

Note that P is undefined at present.

Note also that in order to prove Goedel's completeness theorem, this needs to parametric, that is both phi and psi may contain free variables. The discussion of the incompleteness theorems in Craig Smorinski's article of that name in the "Handbook of Mathematical Logic" edited by Barwise contains an excellent discussion of diagonalisation lemmas.

I'm not going to apply any changes, because I haven't worked out how to typeset equations on Wikipedia yet, and don't really have enough time right now to learn. ---- Charles Stewart 11:32, 19 Aug 2004 (UTC)