- Gödel number
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A number uniquely assigned to each symbol, and to each well-formed formula of some formal language.
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Gödel number
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Gödel number — In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well formed formula of some formal language a unique natural number called its Gödel number. The concept was first used by Kurt Gödel for the proof of his… … 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
Gödel numbering for sequences — A Gödel numbering for sequences provides us an effective way to represent each finite sequence of natural numbers as a single natural number. Of course, the embedding is surely possible set theoretically, but the emphasis is on the effectiveness… … Wikipedia
Gödel, Escher, Bach — Gödel, Escher, Bach: an Eternal Golden Braid … Wikipedia
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
number symbolism — Introduction cultural associations, including religious, philosophic, and aesthetic, with various numbers. Humanity has had a love hate relationship with numbers from the earliest times. Bones dating from perhaps 30,000 years ago show … Universalium
Gödel metric — The Gödel metric is an exact solution of the Einstein field equations in which the stress energy tensor contains two terms, the first representing the matter density of a homogeneous distribution of swirling dust particles, and the second… … Wikipedia
Gödel–Gentzen negative translation — In proof theory, the Gödel–Gentzen negative translation is a method for embedding classical first order logic into intuitionistic first order logic. It is one of a number of double negation translations that are of importance to the metatheory of … Wikipedia
number game — Introduction any of various puzzles and games that involve aspects of mathematics. Mathematical recreations comprise puzzles and games that vary from naive amusements to sophisticated problems, some of which have never been solved.… … Universalium
Gödel numbering — A process whereby a unique number can be associated with any formula of a logical system. This is an essential step in realizing the goal of metamathematics, that the proofs of a system should themselves be treated as mathematical objects. By… … Philosophy dictionary
