Someone can explain me in poor words why we need an x-variant when we deal with the interpretation of quantified formula?
Let s be the value assignment and v the x-variant.
For example M \models_s \forall x A iff M \models_v A for every assignment v that agree with s except possibly at the variable x.
I understand how it works, but i dont catch why we need a second assignment, may we have said "for every assignment s" insteand of "for every assignment v that agree with s"?
And what does it mean "that agree with s except possibly at the variable x"?
