Abstract
The deduction system we will use to show the completeness of first order logic is an extension of the natural deduction systems, presented for propositional logic. There are essentially two other sorts of formal system for mathematical reasoning. Historically, the first one was Hilbert’s system, based on axiom schemes and deduction rules. The second one, due to G. Gentzen, is the sequent calculus which has the advantage of using symmetric deduction rules.
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