Carter,
Thanks for your question, it pointed out to me something I realized I previously thought about but then forgot because I internalized it. The question is:
don’t understand how variables are picked out in the notation AAE\phi
In my mind, this basically deals with the strange binding structure in HyperLTL. I think this is covered in section 3, though probably not as concretely as to answer this question. The answer is that in HyperLTL, variables are not explicitly bound via binders, but instead they are manipulated by means of focus formulas <\phi_1,...,\phi_n> or multi-state propositions
If we have a formula like: