This is really a question about references. The entry in Russian Wikipedia about Hilbert's axioms states, in particular, that completeness of Hilbert's system was proven by Tarski in 1951. The reference is to the Russian encyclopedia of elementary mathematics, to which I don't have access, and I somehow am not able to find any references to this statement in the literature.

I have two questions:

1. The continuity axioms are not first-order-logic statements. What does then completeness mean in this situation?

2. Does anybody know a reference to the original proof by Tarski or any other proof of this statement, for that matter?

This is really a question about references. The entry in Russian Wikipedia about Hilbert's axioms states, in particular, that completeness of Hilbert's system was proven by Tarski in 1951. The reference is to the Russian encyclopedia of elementary mathematics, to which I don't have access, and I somehow am not able to find any references to this statement in the literature.

I have two questions:

1. The continuity axioms are not first-order-logic statements. What does then completeness mean in this situation?

2. Does anybody know a reference to the original proof by Tarski or any other proof of this statement, for that matter?