
Re: Why do we need those real nonconstructible numbers?
Posted:
Nov 9, 2017 12:03 PM


On Thursday, November 9, 2017 at 11:19:02 AM UTC5, WM wrote: > Am Donnerstag, 9. November 2017 14:33:24 UTC+1 schrieb Dan Christensen: > > On Thursday, November 9, 2017 at 1:54:32 AM UTC5, WM wrote: > > > > > There is no countable model of axioms IV and VII. > > > > > > > There is nothing about "model" in the axioms of set theory (e.g. in ZFC). > > There is nothing about "about" and about "axioms" and about many other things in the axioms of ZFC.
In the WP article on ZFC, there are only 9 axioms (including 2 axiom schemas).
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
If you want to show that they are inconsistent (you haven't yet), you will have to be able to both prove and disprove some theorem of ZFC using only these axioms and the ordinary rules of logic (FOL).
> That's because some peripherical knowledge is indispensably required when doing mathematics.
Not at this level. Every assumption must be made explicit. No improvisations or hand waving allowed.
> > > If you want to show that model theory is inconsistent, > > No. Model theory is of no interest. I show that every structure that satisfies the above ZF axioms, usually but not necessarily denoted as a model of these axioms, is uncountable. >
You have failed yet again to demonstrate any inconsistencies in set theory, Mucke. How long have you been at this?
Dan
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