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

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Tucsondrew@me.com

Posts: 806
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


ZG



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