So you agree that “provability oracle for an RE formal system” is the same as “membership oracle for an RE language” and your question is trivial?
ETA: No, first order languages does restrict the set of languages. But I object to this usage. “Formal systems” should include more general systems.
So you agree that “provability oracle for an RE formal system” is the same as “membership oracle for an RE language” and your question is trivial?
ETA: No, first order languages does restrict the set of languages. But I object to this usage. “Formal systems” should include more general systems.