Every first-order logical statement that is true in all models of a set of axioms can be formally derived from those axioms by the usual rules of proof. Proved by Kurt Godel in his 1929 doctoral thesis, it shows first-order provability and first-order semantic truth coincide, in contrast with his later incompleteness theorems for stronger systems.
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StatementIf a first-order sentence is true in every model of a first-order theory T, then there is a first-order proof of that sentence from the axioms of T; semantic truth and syntactic provability coincide for first-order logic. 1 Connections
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Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
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1. Godel's completeness theorem (Wikipedia)
Wikimedia FoundationLead section, first sentence
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.
Lead section, history sentence
It was first proved by Kurt Gödel in 1929.
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