Page "Gödel's completeness theorem" Paragraph 2

There are numerous deductive systems for first-order logic, including systems of natural deduction and Hilbert-style systems.

Common to all deductive systems is the notion of a formal deduction.

This is a sequence ( or, in some cases, a finite tree ) of formulas with a specially-designated conclusion.

The definition of a deduction is such that it is finite and that it is possible to verify algorithmically ( by a computer, for example, or by hand ) that a given collection of formulas is indeed a deduction.