Page "Gödel's completeness theorem" Paragraph 3

A first-order formula is called logically valid if it is true in every structure for the language of the formula.

To formally state, and then prove, the completeness theorem, it is necessary to also define a deductive system.

A deductive system is called complete if every logically valid formula is the conclusion of some formal deduction, and the completeness theorem for a particular deductive system is the theorem that it is complete in this sense.

Thus, in a sense, there is a different completeness theorem for each deductive system.

A converse to completeness is soundness, the fact that only logically valid formulas are provable in the deductive system.