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anticorncob28
Post  Post subject: How can Godel's theorem apply to completely defined systems?  |  Posted: Wed Aug 31, 2016 2:51 am
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According to Gödel's first imcompleteness theorem, any self-consistent system has a statement that is independent of the system.
I don't understand how this is true. Take the real numbers. There are several constructions of the real numbers, and they all demonstrably describe a unique system up to isomorphism. How then can there exist a statement P about the real numbers which can be neither proven nor disproven?
Then you can invent two real number systems, one in which P is true and one in which P is false. But that can't be the case if the two real number constructions are isomorphic.

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GiantEvil
Post  Post subject: Re: How can Godel's theorem apply to completely defined syst  |  Posted: Fri Sep 09, 2016 4:10 am
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https://en.wikipedia.org/wiki/Continuum_hypothesis
Hope this helps.

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