My understanding of the incompleteness theorem is that, for a given set of axioms, there will be unprovably true things. Changing the axioms would change which

My understanding of the incompleteness theorem is that, for a given set of axioms, there will be unprovably true things. Changing the axioms would change which things were unprovable. That being said, here is a much better resource than I am: http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_t...