User blog comment:DontDrinkH20/H-Boogol-Boogol: Hopefully a very big non-salad number/@comment-35470197-20180819021045/@comment-36540075-20180821000613

To answer your first question, see my first answer. I think something is being lost in translation (possibly) in terms of distinct plurality vs. total plurality. There are pleanty of infinite schemas which have only finitely many distinct symbols.

To answer your second question, standard semantics is well-defined on classes using second-order logic to define it. It is defined exactly like it is defined for set-sized models.