I did mean “semantically valid” to be “true in all models”, I was just thinking about second-order Peano arithmetic not first-order ;) I think it’s more natural precisely because then it exactly does show incompleteness.
I did mean “semantically valid” to be “true in all models”, I was just thinking about second-order Peano arithmetic not first-order ;) I think it’s more natural precisely because then it exactly does show incompleteness.