Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. It makes a close link between model theory that deals with what is true in different models, and proof theory that studies what can be formally proved in particular formal systems.
It was first proved by Kurt Gödel in 1929. It was then simplified in 1947, when Leon Henkin observed in his Ph.D. thesis that the hard part of the proof can be presented as the Model Existence Theorem (published in 1949). Henkin's proof was simplified by Gisbert Hasenjaeger in 1953.
Read more about Gödel's Completeness Theorem: Consequences, Relationship To The Incompleteness Theorem, Relationship To The Compactness Theorem, Completeness in Other Logics, Proofs
Famous quotes containing the words completeness and/or theorem:
“Poetry presents indivisible wholes of human consciousness, modified and ordered by the stringent requirements of form. Prose, aiming at a definite and concrete goal, generally suppresses everything inessential to its purpose; poetry, existing only to exhibit itself as an aesthetic object, aims only at completeness and perfection of form.”
—Richard Harter Fogle, U.S. critic, educator. The Imagery of Keats and Shelley, ch. 1, University of North Carolina Press (1949)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)