Editing Gödel's completeness theorem (section)

==Proofs==
Gödel's [[Original proof of Gödel's completeness theorem|original proof of the theorem]] proceeded by reducing the problem to a special case for formulas in a certain syntactic form, and then handling this form with an ''ad hoc'' argument.

In modern logic texts, Gödel's completeness theorem is usually proved with [[Leon Henkin|Henkin]]'s proof, rather than with Gödel's original proof. Henkin's proof directly constructs a [[term model]] for any consistent first-order theory. James Margetson (2004) developed a computerized formal proof using the [[Isabelle (theorem prover)|Isabelle]] theorem prover.<ref>{{cite report | url=http://afp.sourceforge.net/entries/Completeness-paper.pdf |archive-url=https://web.archive.org/web/20060222105036/http://afp.sourceforge.net/entries/Completeness-paper.pdf |archive-date=2006-02-22 |url-status=live | author=James Margetson | title=Proving the Completeness Theorem within Isabelle/HOL | type=Technical Report | date=Sep 2004 }}</ref> Other proofs are also known.