I was just reading up about turing degrees and the part marked in red confused me:
If there was a non computably enumerable turing machine that could be computed given the computably enumerable set as an oracle - shouldn't it also be possible to simply c.e. this second set in the first turing machine instead and use it? And wouldn't that make the first set also computably enemerable?
Probably I'm messing something up here, but I really can't seem to figure it out. I'd be really thankful if anyone could tell me, what I'm getting wrong here. Thank you in advance and have a nice day!