I am currently taking a class in complexity theory and I am struggling with this question.
We define a TM with Oracle per. Sipser 6.18 as:
"An oracle for language $B$ is an external device that is capable of reporting whether any string $w$ is a member of $B$. An oracle Turing machine is a modified Turing machine that has the additional capability of querying an oracle. We write $M^b$ to describe an oracle Turing machine that has an oracle for language B."
I think that the answer is potentially false. We know that the set of languages is uncountable and suppose we had a Oracle Turing machine that accepts if the oracle answers YES, reject otherwise. Wouldn't that mean that then the set of languages recognized by TM with an oracle be uncountable?