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In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory.
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second-order logic first-order set semantics displaystyle theory variables domain sets formulas theorem henkin real numbers sentence finite sort standard quantification
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Second-order logic | is a | extension of first-order logic | 0.90 | text |
| second-order arithmetic | instance of | Lindström's theorem imports that Henkin models are just disguised first-order models.For theories | 0.80 | text |
| the existence of non-standard interpretations of higher-order domains isn't just a deficiency of the particular axiomatisation derived from type theory that Henkin used | instance of | Lindström's theorem imports that Henkin models are just disguised first-order models.For theories | 0.80 | text |
| but a necessary consequence of Gödel's incompleteness theorem | instance of | Lindström's theorem imports that Henkin models are just disguised first-order models.For theories | 0.80 | text |
| Second-order logic | related to Deductive systems | Several | 0.60 | section |
| Second-order logic | related to Deductive systems | Each | 0.60 | section |
| Second-order logic | related to Deductive systems | The | 0.60 | section |
| Second-order logic | related to Deductive systems | This | 0.60 | section |
| Second-order logic | related to Definition of equality | Objects | 0.60 | section |
| Second-order logic | related to Definition of equality | In | 0.60 | section |
| Second-order logic | related to Expressive power | Second-order | 0.60 | section |
| Second-order logic | related to Expressive power | For | 0.60 | section |
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