I’m pretty sure that’s what he means.
I think that he means something analogous to the way that we can add some axioms involving the symbol “+” to the Peano axioms, and then show in second-order logic that the new axioms define addition uniquely.
I think that he means something analogous to the way that we can add some axioms involving the symbol “+” to the Peano axioms, and then show in second-order logic that the new axioms define addition uniquely.