Proofs
Gödel's 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 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. Other proofs are also known.
Read more about this topic: Gödel's Completeness Theorem
Famous quotes containing the word proofs:
“Would you convey my compliments to the purist who reads your proofs and tell him or her that I write in a sort of broken-down patois which is something like the way a Swiss waiter talks, and that when I split an infinitive, God damn it, I split it so it will stay split, and when I interrupt the velvety smoothness of my more or less literate syntax with a few sudden words of bar- room vernacular, that is done with the eyes wide open and the mind relaxed but attentive.”
—Raymond Chandler (1888–1959)
“Trifles light as air
Are to the jealous confirmation strong
As proofs of holy writ.”
—William Shakespeare (1564–1616)
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—H.L. (Henry Lewis)