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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Goedel Completeness Theorem
Replies: 4   Last Post: Dec 29, 2009 9:35 AM

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Calvin

Posts: 343
Registered: 10/27/06
Re: Goedel Completeness Theorem
Posted: Dec 26, 2009 10:29 PM
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On Dec 26, 3:42 pm, "gabe2...@gmail.com" <gabe2...@gmail.com> wrote:
> I am reading "Set Theory and the Continuum Hypothesis" by Paul Cohen.
> In it he states the Goedel Completeness Theorem:
>
> Let S be any consistent set of statements.  Then there exists a model
> for S whose cardinality does not exceed the cardinality of the number
> of statements in S if S is infinite and, and is countable if S is
> finite.
>
> The version of the theorem from the Stanford Encyclopedia of
> Philosophy states:
>
> Every valid logical expression is provable.
>
> Are these equivalent statements?
>
> Thanks,
> Gabriel Read

yes and no

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