> Am Mittwoch, 8. November 2017 14:40:07 UTC+1 schrieb Alan Smaill: >> WM <email@example.com> writes: >> >> > No. There is no model dependence. First we have to guarantee that >> > omega is there and simultaneously P(omega) will be there. And then we >> > can look for a model satisfying that requirement. >> >> This is truly miraculous: > > No, it is an axiom.
Keep the jokes coming.
> The axiom does not depend on any model. > > Axiom IV. Jeder Menge T entspricht eine zweite Menge ?T (die > "Potenzmenge" von T), welche alle Untermengen von T und nur solche als > Elemente enthält. [E. Zermelo: "Untersuchungen über die Grundlagen der > Mengenlehre I", Math. Ann. 65 (1908) p. 265] "Every set T is related > to a second set ?(T) (the 'power set' of T), which contains all > subsets of T and only those as elements."
Of course the axiom does not depend on the model.
But the models simply have to respect the axiom, in that all the collections *that happen to be sets* and where every element is in X will be in the power set of X.
More than that is achieved only by Magical Incantation,
>> Who needs proof when we have WM's Infallible Judgement? >> >> "No proof is required": that was His catchphrase. > > You confuse things. I said "no axioms are required".
Your memory fails you now.
You told us that no proof is required to show that the set of even numbers is a subset of |N. You were certainly unable to provide such a proof.