On clarification of intersection of classes definition How do you define $\oplus P\cap PP$? 


$L\in\oplus P$ iff $\exists\mbox{ NTM }M:\forall x,\#acc_M(x)\mod2\equiv0$.
$L\in PP$ iff $\exists\mbox{ NTM }M:\forall x,\#acc_M(x)&gt;\#rej_M(x)$.


Consider the classes $C_1,C_2,C_3$.

$L\in C_1$ iff $\exists\mbox{ NTM }M:\forall x\#acc_M(x)&gt;\#rej_M(x)\mbox{ and }\#acc_M(x)\mod2\equiv0$?

$L\in C_2$ if $\exists\mbox{ NTM }M_1:\forall x\#acc_{M_1}(x)&gt;\#rej_{M_1}(x)\mbox{ and }\#acc_{M_1}(x)\mod2\equiv0$ and $L\not\in C_2$ if $\exists\mbox{ NTM }{M_2}:\forall x\#acc_{M_2}(x)\leq \#rej_{M_2}(x)\mbox{ and }\#acc_{M_2}(x)\mod2\equiv1$.

$\exists\mbox{ NTM }M'$ such that
$L\in C_3$ if $\forall x\#acc_{M_1}(x)&gt;\#rej_{M'}(x)\mbox{ and }\#acc_{M'}(x)\mod2\equiv0$ and $L\not\in C_3$ if $\forall x\#acc_{M'}(x)\leq \#rej_{M'}(x)\mbox{ and }\#acc_{M'}(x)\mod2\equiv1$.

Which of $C_1,C_2,C_3$ defines $\oplus P\cap PP$ and which one $\oplus P\wedge PP$? What about last one?
Complexity classes are sets of languages. Intersection of sets is intersection of sets.