Enderton's 'Mathematical Introduction to Logic' X with an arrow on top notation.

Question

I should like to know what the notation of an 'X' with an arrow on top of it means in the context of Enderton's aforementioned book, since its introduction, at least as far as I've noticed, is not really explained. It appears, for instance, in the following context, in which 'X' is a broken representation of the symbol: "For each of the 2² pairs X, we set Bα(X) equal to the truth value α receives when its sentence symbols are given the values indicated by X."

Thanks in advance.

Answer 1

Typically $\vec X$ is a vector of values. Since the word pair here is used, I would expect $\vec X = (X_1,X_2)$. More generally, $\vec X = (X_1,\ldots,X_n)$. In this case, it appears to be a vector of truth values, so each $X_i$ is 0 or 1, or $\top$ or $\bot$, or true or false, or something like that.