Re: Which theories hold a true but unprovable statement?

On Mon, 12 Feb 2007 19:05:48 -0500, herbzet <herbzet@xxxxxxxxx> said:
george wrote:

Of course, but IN A DECIDABLE RECURSIVELY AXIOMATIZABLE
FIRST-ORDER THEORY, YOU DON'T need to consider any models
to discern the truth or falsity of any sentence. EVERY SENTENCE
in such theories is true (xor false) IN EVERY model of the theory,

Every sentence of every theory is true in every model of that theory.

I think he means to be saying that every sentence in the *language* of a
decidable, axiomatizable first-order theory is either true in all models
of the theory or false in all models of a theory. Of course, that's
false in general. He appears to be confusing decidability with
completeness.

.