KnowraGödel's incompleteness theoremsLinked fromLinked fromThe 58 pages that link to Gödel's incompleteness theorems, each with the reason it gives.All 58Broader topic 9Related 36Narrower topic 4Compared with 9Gödel numberingBroader topic: Gödel used number codes to express statements about formal proofs within arithmetic.Kurt GödelBroader topic: These are the central results Gödel established using arithmetized syntax.TheoremBroader topic: They establish limits on which mathematical statements formal systems can prove.Self-referenceBroader topic: Gödel encoded a sentence that, informally, says it is not provable in its system.History of logicBroader topic: They changed expectations about whether mathematics could be captured by a complete formal system.Formal scienceBroader topic: They demonstrate fundamental limits on what formal proof systems can establish.CodeBroader topic: Gödel coding makes formal syntax available to arithmetic.Douglas HofstadterBroader topic: Hofstadter uses their self-referential structure as a model for discussions of minds.Mathematical conceptsBroader topic: They establish limits on what formal mathematical systems can prove.