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

Ill-defined.

Only a single variable symbol? Then it is impossible to assume ZFC. How do you encode a statement as a variable?

What does "true" mean? Truth is not definable under ZFC.

What does "x satisfies y" for sets x and y mean? Sets are not properties. Also, satisfaction is not definable. Moreover, you do not have a variable symbol y. Since you do not allow constant term symbol, y should be x or f(x) for some function formula f.

What is "the axioms declared by Tx as well as the axioms of ZFC"? Axiom with free occurence of a variable of sets and statements? Then contradiction.

What does "all-knowing oracle" mean? Maybe you do not know what orcle precisely means.

According to the use of intuitive notions, I am certain that you do not understand set theory. I strongly recommend to use stuffs which you actually understand.