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Topic: Matheology § 291
Replies: 28   Last Post: Jun 19, 2013 5:29 PM

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Posts: 1,053
Registered: 5/24/13
Re: Matheology § 291
Posted: Jun 17, 2013 12:59 PM
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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.

> Regards, WM


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