
Re: Why do we need those real nonconstructible numbers?
Posted:
Nov 9, 2017 1:54 AM


Am Mittwoch, 8. November 2017 23:52:42 UTC+1 schrieb Dan Christensen:
> > It convinces us of the fact that set theory can cause real brain damage. Of course you cannot be healed. But discussions like these are very helpful in convincing normal people including young students that set theory is really detrimental to clear thinking. > > > Brave words for someone who time and again has claimed to have found inconsistencies in set theory, but could not prove it in using the axioms of set theory as would be required.
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 ?(T) (the '"power set" of T), which contains all subsets of T and only those as elements.
A model of a theory is a structure that satisfies the sentences of that theory, in particular its axioms.
There is no countable model of axioms IV and VII.
Regards, WM

