[p0llard]

> Gödel's statements are true in all models

This is wrong, and I said the exact opposite of this: there are non-standard models of PA in which G_F is false.

There is a fundamental difference between Gödel sentences and AoC, which is that the Gödel sentence is Pi_1, which means its independence implies its truth in the standard model.

I'm just not really a fan of unqualified "true" meaning "true in the standard model"; I think if you're doing a course purely on the incompleteness theorems for an audience without much exposure to mathematical logic, using "true to refer to "truth in the standard model" is not a good idea and is likely to lead to misconceptions.

Perhaps the fact that you think G_F is true in all models is evidence in favour of my claim?