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- Gödel's_incompleteness_theorems abstract "Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem.The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.".
- Gödel's_incompleteness_theorems wikiPageID "58863".
- Gödel's_incompleteness_theorems wikiPageRevisionID "606581568".
- Gödel's_incompleteness_theorems id "p/g044530".
- Gödel's_incompleteness_theorems title "Gödel incompleteness theorem".
- Gödel's_incompleteness_theorems subject Category:Epistemology.
- Gödel's_incompleteness_theorems subject Category:Mathematical_logic.
- Gödel's_incompleteness_theorems subject Category:Metatheorems.
- Gödel's_incompleteness_theorems subject Category:Model_theory.
- Gödel's_incompleteness_theorems subject Category:Proof_theory.
- Gödel's_incompleteness_theorems subject Category:Theorems_in_the_foundations_of_mathematics.
- Gödel's_incompleteness_theorems comment "Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics.".
- Gödel's_incompleteness_theorems label "Gödel's incompleteness theorems".
- Gödel's_incompleteness_theorems label "Gödelscher Unvollständigkeitssatz".
- Gödel's_incompleteness_theorems label "Onvolledigheidsstellingen van Gödel".
- Gödel's_incompleteness_theorems label "Teoremas da incompletude de Gödel".
- Gödel's_incompleteness_theorems label "Teoremas de incompletitud de Gödel".
- Gödel's_incompleteness_theorems label "Teoremi di incompletezza di Gödel".
- Gödel's_incompleteness_theorems label "Théorèmes d'incomplétude de Gödel".
- Gödel's_incompleteness_theorems label "Twierdzenie Gödla".
- Gödel's_incompleteness_theorems label "Теорема Гёделя о неполноте".
- Gödel's_incompleteness_theorems label "مبرهنات عدم الاكتمال لغودل".
- Gödel's_incompleteness_theorems label "ゲーデルの不完全性定理".
- Gödel's_incompleteness_theorems label "哥德尔不完备定理".
- Gödel's_incompleteness_theorems sameAs G%C3%B6del's_incompleteness_theorems.
- Gödel's_incompleteness_theorems sameAs Gödelovy_věty_o_neúplnosti.
- Gödel's_incompleteness_theorems sameAs Gödelscher_Unvollständigkeitssatz.
- Gödel's_incompleteness_theorems sameAs Θεωρήματα_μη_πληρότητας_του_Γκέντελ.
- Gödel's_incompleteness_theorems sameAs Teoremas_de_incompletitud_de_Gödel.
- Gödel's_incompleteness_theorems sameAs Théorèmes_d'incomplétude_de_Gödel.
- Gödel's_incompleteness_theorems sameAs Teoremi_di_incompletezza_di_Gödel.
- Gödel's_incompleteness_theorems sameAs ゲーデルの不完全性定理.
- Gödel's_incompleteness_theorems sameAs 불완전성_정리.
- Gödel's_incompleteness_theorems sameAs Onvolledigheidsstellingen_van_Gödel.
- Gödel's_incompleteness_theorems sameAs Twierdzenie_Gödla.
- Gödel's_incompleteness_theorems sameAs Teoremas_da_incompletude_de_Gödel.
- Gödel's_incompleteness_theorems sameAs Q200787.
- Gödel's_incompleteness_theorems sameAs Q200787.
- Gödel's_incompleteness_theorems wasDerivedFrom Gödel's_incompleteness_theorems?oldid=606581568.