On $UP$, $NP$, $\oplus P$ and $PP$? We know $UP\subseteq NP\subseteq PP$.


  Is $UP^{\oplus P}\subseteq NP^{\oplus P}\subseteq PP^{\oplus P}$?


I think the first $UP^{\oplus P}\subseteq NP^{\oplus P}$ is straightforward since whatever queries an $UP$ machine can do we know an $NP$ machine can do.


  How to show second $NP^{\oplus P}\subseteq PP^{\oplus P}$?
Consider the oracle machine $N$ that decides $L \in NP^{\oplus P}$. For each computational branch of $N$, if it ends with $\textsf{YES}$, do nothing. If it ends with $\textsf{NO}$, branch and output once $\textsf{YES}$ and once $\textsf{NO}$. Therefore, $L\in  PP^{\oplus P}$.