User blog comment:Ubersketch/Uncomputable function/@comment-35470197-20190618223755/@comment-35470197-20190618232445

You have not defined how to encode a statement as a variable.

> True means that the statement is being assumed.

Then satisfaction is ill-defined again.

> And contradiction goes under "fails to produce a number."

I pointed out the contradiction because I guessed that you do not intend it. But if you allow the contradiction.

Do you understand what "definable" means? In order to encode a natural number n in the formalised set theory, you actually need more than n symbols.

Also, ""And contradiction goes under "fails to produce a number." "" is false. Contradition does not mean it. Whether it fails or not depends on the axiom of base theory, which is unspecified. What axiom do you assume in the base theory? You just declared Tx + ZFC in the formalised theory.

> All-knowing oracle is just a word I used for something that has everything that can be proved in a system.

Circular logic. Since you introduced a theory which is not the usual one, i.e. the first or second order logic, you need to precisely define the notion of a proof.