Re: Gödel's theorems in Wikipedia

Aatu Koskensilta <aatu.koskensilta@xxxxxxxxx> wrote:
>I took the time to rewrite the three first sections of the rather sorry
>Wikipedia entry on Gödel's incompleteness theorems
>(http://en.wikipedia.org/wiki/G%F6del%27s_incompleteness_theorem). Any
>corrections or suggestions would be appreciated.

Aatu, I have a suggestion for the definition of omega-consistency in the
first section of the article; the one you provided seems to me a bit
hard to parse. Currently, it reads:

Omega-consistency is a technical concept which applies to a theory T if
T does not prove for any property P that there exists a number with a
property P and simultaneously prove for every natural number n that n
does not have the property P.

I suggest:

Omega-consistency is a technical concept which applies to a theory T if,
for no property P, (i) T proves the general proposition that there
exists some number with the property P, but (ii) for every specific
natural number n, T proves that n does not have the property P.

It also strikes me that the sentence that follows in that paragraph
(which is intended to clarify the second part of the definition) becomes
unnecessary with this change.

Also, the second paragraph in that section might fit better in the
section "Misconceptions about Gödel's Theorem."

And I still think someone ought to just clobber the section on "The
Meaning of Gödel's Theorem", which is a mess, especially in contrast
with your sections on the incompleteness theorem and the nice new
section (yours also?) on Gentzen's Theorem.

Chris Menzel

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