On Monday, June 17, 2013 5:23:11 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Monday, 17 June 2013 07:43:58 UTC+2, Zeit Geist wrote: > > > In some systems consisting of ZFC + Some "Large Cardinal Axiom" CH, even GHC, can be proved or disproved. Perhaps Godel foresaw the coming power of Inner Model Theory and Descriptive Set Theory. > > > > In some axiom systems it is possible to prove that the reals can be well-ordered, in other axiom-systems it is possible to prove that the reals cannot be well-ordered. This shows that these "proofs" are nonsense, only pursued by matheologians. No science would rely on modern logic. >
Why are you talking about the well-ordering of the reals? I thought this was about the Continuum Hypothesis?
> > The question is simply whether the reals can be well-ordered or not. But that question is not decided by matheology. >
That is not the question of the Continuum Hypothesis.
It's about the Cardinality of the Real Numbers, not about whether its well-ordered or not.
The Well-Ordering Principle is related to the Axiom of Choice.
Looking at the article, I'm sure you realize this. I'm just wondering why you're bring up the well-ordering of the reals.
> > How can some people remain that stupid to give a dime for a "proof" in matheology after Zermelo's desaster has become general knowledge? (Zermelo thought to prove that it can be done. Fraenkel wrote that *hitherto* nobody had accomplished it.) Menawhile the value of modern logic should be obvious to everybody. >
Are you talking about well-ordered sets again?
Everyone now knows "Every set can Well-Ordered" is independent of ZF. As is the Continuum Hypothesis of ZF or ZFC.
I know that the idea of a statement that is logically independent of a given set of axioms can be confusing.