It doesn’t have to be a finite set of axioms just recursively enumerable. The first order Peano axioms are not finite in number. One of them is an axiom schema. (I believe.)
You’ve given excellent explanations on this topic. It’s rare that someone writes about the meaning of the Incompleteness theorems correctly. I think it’s worth pointing out or adding that when talking about The Natural…
It doesn’t have to be a finite set of axioms just recursively enumerable. The first order Peano axioms are not finite in number. One of them is an axiom schema. (I believe.)
You’ve given excellent explanations on this topic. It’s rare that someone writes about the meaning of the Incompleteness theorems correctly. I think it’s worth pointing out or adding that when talking about The Natural…