[rfugger]

Unfortunately, restricting to only computable maths means disallowing the natural numbers, basic arithmetic, or any equivalent structure, since Gödel incompleteness would apply. I doubt any system without access to the full set of natural numbers or basic arithmetic could qualify as "general AI".

[asdfasgasdgasdg]

Pardon my ignorance. Computers appear to be able to perform basic arithmetic. For example, you can open up the console in your browser and find that the sum of two and two is indeed four. So it is not entirely obvious to me how basic arithmetic is non-computable.

[krastanov]

If you permit infinitely many integers it becomes problematic. If you are dealing with a finite entity (e.g. the finite part of the universe that can affect us), then there are no problems.

[rfugger]

Gödel incompleteness applies to any system capable of basic arithmetic.