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Re: Tim Chow in Forcing for dummies
Posted:
Nov 8, 2017 12:29 PM


WM <wolfgang.mueckenheim@hsaugsburg.de> writes:
> Am Mittwoch, 8. November 2017 17:35:11 UTC+1 schrieb Alan Smaill: > > >> 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. > > The models have to respect these axioms (among others): > > Axiom VII. The domain contains at least a set Z which contains the > nullset as an element and is such that each of its elements a is > related to another element of the form {a}, or which with each of its > elements a contains also the related set {a} as an element. > > Axiom IV. Every set T is related to a second set U(T) (the 'power > set' of T), which contains all subsets of T and only those as > elements. > > Therefore { }, {{ }}, {{{ }}}, ... happen to be sets in every > model. And all combinations of these sets happen to be sets,
Non sequitur.
Try and prove that in ZF  you claim it holds in all models; it follows that it has an FOL proof. Find that proof, and you have inconsistency of ZF.
Try again. Fail again.
"No proof required": that was his catchphrase.
 Alan Smaill



