What does a quantifier with a subscript mean?

Question

Is there a difference between $\forall x$ and $\forall_{x}$?

I saw someone write $\forall_{x} \text{ Qt}(x)$, and I want to know whether that is the same as $\forall x \text{ Qt}(x)$.

Answer 1

It is just a different notational convention.

It comes from following the format of a conjunctive series, $\bigwedge_x Q(x)$, which was once used as notation for universal quantification. $~\forall x~Q(x)$ is the most current convention, although the transition form, $\forall_x Q(x)$, is still being used in some texts to date.