I have a question regarding a definition in Kanamori's book on page 136. (it's the beginning of the subsection about Random Reals)
Let $\mathcal{B}^{\star} = \{X \in \mathcal{B} \ \lvert \ X \ \text{is not null} \}$ where $\mathcal{B}$ denotes the Borel-Sigma-algebra. One defines the forcing partial order for $p,q \in \mathcal{B}^{\star}$ by:
$p \leq q \leftrightarrow p \subseteq q$
Then there is the following exercise:
(a) for $p,q \in \mathcal{B}^{\star} \ p$ and $q$ are incompatible iff $p \cap q$ is null.
(b) $\mathcal{B}^{\star}$ has the $\omega_1$-chain condition.
My question: in my opinion there is a mistake in the definition of the partial order. Shouldn't it be $p \leq q \leftrightarrow p \supseteq q$?
Thank you very much for any help in advance.