Re: FOL & completeness



MoeBlee wrote:

That should be corrected slightly:

The completeness theorem is that if a formula is satisfied by ALL
models then the formula is provable.


iff, for a first order theory




The incompleteness theorem is that for any consistent, recursive set of
axioms, there is a sentence that is true in the standard model of
number theory (but NOT true in all models) that is not provable from
said axioms.

So, can we say that the same Goedel theorem affirms that G is not logically
valid ?


.

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