User blog comment:Ubersketch/Uncomputable function/@comment-35470197-20190618223755/@comment-35470197-20190619220629

> My symbols follow whatever rules they follow in first order logic, save for Tx which is used to declare axioms.

First order logic is not a logic which gives rules on symbols. It just gives syntax and formulate proofs. As I recommended above, please use stuffs which you actually know the definition.

Such an intuitive explanation does not give a precise defintion of proofs in your original formal system.

> I've decided to change the oracle to just something able to solve any problem given a mathematical system.

I guess that it will be ill-defined by well-known problems such as Tarskian paradox. At least, you need to correct definitions without intuition-based unformalised explanation.

Well, this is the third time to ask it. What is the axiom of base theory? Why you avoid answering it? Without fixing the axiom, no argument makes sense.