
Re: Why do we need those real nonconstructible numbers?
Posted:
Nov 11, 2017 2:11 PM


Am Samstag, 11. November 2017 11:07:06 UTC+1 schrieb Zelos Malum: > Den lördag 11 november 2017 kl. 10:32:09 UTC+1 skrev WM: > > Am Freitag, 10. November 2017 19:50:36 UTC+1 schrieb Dan Christensen: > > > On Friday, November 10, 2017 at 9:53:06 AM UTC5, WM wrote: > > > > > > > > > > > > Therefore we use only FOL and the axioms of ZF and find that they make ZF uncountable without refering to anything else (that others may call a model but that you don't know and that threfore should not be used when talking to you). > > > > > > To prove that ZFC is inconsistent, you must be able to both prove and disprove the same theorem using only FOL and the axioms ZFC. > > > > No. My share is done, showing that the power set of the set defined in Axiom VII is uncountable. The other part has been settled by Skolem already. > > > > > > > No improvisations or hand waving allowed. > > > > Where is that detected? In Skolem's proof? In Hessenbergs proof using axioms VII and IV without any models? > > > The fact that 2^N is uncountable is not an issue in mathematics.
And the fact that N or Z or an equivalent set is in every model of ZF is not an issue either.
Regards, WM

