Re: completeness of predicate calculus


falcon wrote:
I am currently reading Rebecca Goldstein's "Incompleteness" (The Proof
and Paradox of Kurt Godel). I was surprised to read that Godel's PhD
dissertation had been on the completeness of predicate calculus (which
she called limpid calculus). What exactly does it mean for predicate
calculus to be complete? The only reason I even know predicate
calculus is because of references to it when I studied relational
databases back in undergrad.

It means that every statement which is true in all models is provable.
It doesn't mean that for every statement A, either A or ~A is provable
- that's a different sort of completeness.

.

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