Okay. I’m just trying to get a sense of what kind of questions all of this is meant to answer. It sounds like we start with “SI is uncomputable, but is computable relative to some oracle”. Now we want to say “this machine I have built out of SI is still computable relative to that same oracle”. That kind of thing? And you’re saying here that while the machine built out of SI is not a function from reals to reals, we can prove these statements by classifying functions from reals to reals involved in its construction.
Okay. I’m just trying to get a sense of what kind of questions all of this is meant to answer. It sounds like we start with “SI is uncomputable, but is computable relative to some oracle”. Now we want to say “this machine I have built out of SI is still computable relative to that same oracle”. That kind of thing? And you’re saying here that while the machine built out of SI is not a function from reals to reals, we can prove these statements by classifying functions from reals to reals involved in its construction.