To every

*w*-consistent recursive class k of formulae there correspond recursive class-sings r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg(k) (where v is the free variable of r).

which translates to

All consistent axiomatic formulations of number theory include undecidable propositions.

...

Godel showed that provability is a weaker notion than truth, no matter what axiomatic system is involved.

...

## 2 comments:

All consistent axiomatic formulations of number theory include undecidable propositions.

I also like the following:

Any axiomatic system of number theory is either incomplete or inconsistent.Copied this over from Amar's blog.

An year of incompleteness

Post a Comment