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Calvin
Posts:
351
Registered:
10/27/06


Re: Goedel Completeness Theorem
Posted:
Dec 26, 2009 10:29 PM


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



