I'm having some trouble understanding the following proposition:
Let $\mathcal M$ be an $\cal L$-structure. if $X \subset M^n$ is $A$-definable, then every $\cal L$-automorphism of $M$ that fixes A pointwise fixes X setwise (that is, if $\mu$ is an automorphism of $M$ and $\mu (a) = a$ for all $a \in A$, then $\mu (X) = X$).
If $\mu : M \to M$ is an automorphism of $M$, how is $\mu (X)$ or $\mu (a)$ even defined? $X\subset M^n$ and $A\subset X^l$ in this context for some $n$ and $l$.
Is this an error the author of the book made, or is this standard notation in model theory?
thank you