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- Completeness_(logic) abstract "Completeness is a fundamental concept in metalogic, and the term may be used without qualification with differing meanings depending on the context within mathematical logic. A logical system is complete with respect to a particular property if and only if every formula, (or proposition) derived using that system (called theorems) has that particular property. Kurt Gödel, Leon Henkin, and Emil Leon Post all published proofs of completeness. (See History of the Church–Turing thesis.) Completeness, as a quality of logical systems, is closely related to consistency. A formal system is consistent if, for all formulas φ of the system, the formulas φ and ¬φ (the negation of φ) are not both theorems of the system (that is, they cannot be both proved with the rules of the system).A logical system which is not complete is said to be incomplete. The axioms of Euclidean geometry without the parallel postulate are an example of an incomplete logical system.".
- Completeness_(logic) wikiPageID "31271451".
- Completeness_(logic) wikiPageRevisionID "606006481".
- Completeness_(logic) subject Category:Mathematical_logic.
- Completeness_(logic) subject Category:Metalogic.
- Completeness_(logic) subject Category:Model_theory.
- Completeness_(logic) subject Category:Proof_theory.
- Completeness_(logic) comment "Completeness is a fundamental concept in metalogic, and the term may be used without qualification with differing meanings depending on the context within mathematical logic. A logical system is complete with respect to a particular property if and only if every formula, (or proposition) derived using that system (called theorems) has that particular property. Kurt Gödel, Leon Henkin, and Emil Leon Post all published proofs of completeness.".
- Completeness_(logic) label "Completeness (logic)".
- Completeness_(logic) label "Completezza (logica matematica)".
- Completeness_(logic) label "Completude (lógica)".
- Completeness_(logic) label "Vollständigkeit (Logik)".
- Completeness_(logic) label "完全性".
- Completeness_(logic) sameAs Vollständigkeit_(Logik).
- Completeness_(logic) sameAs Completezza_(logica_matematica).
- Completeness_(logic) sameAs 完全性.
- Completeness_(logic) sameAs Completude_(lógica).
- Completeness_(logic) sameAs m.010f8ptj.
- Completeness_(logic) sameAs Q15846555.
- Completeness_(logic) sameAs Q15846555.
- Completeness_(logic) wasDerivedFrom Completeness_(logic)?oldid=606006481.
- Completeness_(logic) isPrimaryTopicOf Completeness_(logic).