Gödel's theorem(s)
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Philosophy dictionary. . 2011.

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  • Gödel's theorem(s) — Gödel s first incompleteness theorem states that for any consistent logical system S able to express arithmetic there must exist sentences that are true in the standard interpretation of S, but not provable. Moreover, if S is omega consistent… …   Philosophy dictionary

  • 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's theorem — may refer to: *Gödel s incompleteness theorems *Gödel s completeness theorem …   Wikipedia

  • gödel's theorem — noun also gödel s incompleteness theorem ˈgœ̅dəlz Usage: usually capitalized G Etymology: after Kurt Gödel died 1978 American mathematician : a theorem in advanced logic: in any logical system as complex or more complex than the arithmetic of the …   Useful english dictionary

  • Godel's theorem — noun Etymology: Kurt Gödel died 1978 American mathematician Date: 1933 a theorem in advanced logic: in any logical system as complex as or more complex than the arithmetic of the integers there can always be found either a statement which can be… …   New Collegiate Dictionary

  • Godel’s Theorem — all branches of mathematics are based on propositions that can’t be proved within that branch (named for mathematician Kurt Godel) …   Eponyms, nicknames, and geographical games

  • Gödel's theorem — /ˈgɜdəlz θɪərəm/ (say gerduhlz thearruhm) noun the proposition that in a formal axiomatic system, such as logic or mathematics, it is impossible to prove consistency without using methods beyond those of the system itself. {from Kurt Gödel,… …   Australian English dictionary

  • Löb's theorem — In mathematical logic, Löb s theorem states that in a theory with Peano arithmetic, for any formula P, if it is provable that if P is provable then P , then P is provable. I.e.:if PA vdash Bew(# P) ightarrow P, then PA vdash Pwhere Bew(#P) means… …   Wikipedia

  • Rosser's theorem — This article is about a theorem in number theory. For the Gödel ndash;Rosser incompleteness theorems, see Gödel s incompleteness theorems and Rosser s trick. In number theory, Rosser s theorem was proved by J. Barkley Rosser in 1938. Its… …   Wikipedia

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