 Gödel's incompleteness theorem

A theorem in mathematical logic that states that no consistent system can be used to prove its own consistency.
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Godel's incompleteness theorem — noun see Godel s theorem … New Collegiate Dictionary
Gödel's incompleteness theorem — Logic, Math. 1. the theorem that states that in a formal logical system incorporating the properties of the natural numbers, there exists at least one formula that can be neither proved nor disproved within the system. 2. the corollary that the… … Universalium
gödel's incompleteness theorem — noun see gödel s theorem … Useful english dictionary
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 was first proved by Kurt Gödel in 1929. A first order formula is called logically valid if… … Wikipedia
Gödel's incompleteness theorems — In mathematical logic, Gödel s incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. The theorems are of… … Wikipedia
incompleteness theorem — noun Logic the theorem, proposed by the mathematician Kurt Gödel, that in any sufficiently powerful, logically consistent formulation of logic or mathematics there must be true formulas which are neither provable nor disprovable … English new terms dictionary
Proof sketch for Gödel's first incompleteness theorem — This article gives a sketch of a proof of Gödel s first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses which are discussed as needed during the sketch. We will assume for the… … Wikipedia
Gödel's theorem — n. either of two theorems published by the mathematician Kurt Gödel in 1931 that prove all mathematical systems are incomplete in that their truth or consistency can only be proved using a system of a higher order: also called Gödel s proof or… … Universalium
Gödel's theorem — n. either of two theorems published by the mathematician Kurt Gödel in 1931 that prove all mathematical systems are incomplete in that their truth or consistency can only be proved using a system of a higher order: also called Gödel s proof or… … English World dictionary
Gödel, Kurt — born April 28, 1906, Brünn, Austria Hungary died Jan. 14, 1978, Princeton, N.J., U.S. Austrian born U.S. mathematician and logician. He began his career on the faculty of the University of Vienna, where he produced his groundbreaking proof (see… … Universalium