[FOM] alleged quote from Hilbert

[John McCarthy]

It seems to me that consistency is not enough in a very simple way.
Suppose some alleged axioms for (say) group theory were consistent but 
admitted only one model - the trivial group.  That would be quite
unsatisfactorry.  It seems that a set of axioms needs to have enough
models.

For a propositional calculus theory, I know how to parameterize the
set of all models in a simple way, but I don't know how to do it for
even monadic predicate calculus.