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In logic, a metatheorem is a statement about a formal system proven in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved within a metatheory, and may reference concepts that are present in the metatheory but not the object theory.[citation needed]
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system logic formal proved metatheory theory citation metatheorems set may needed language used particular sentences class axioms theorem arithmetic provable
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Metatheorem | is a | statement about a formal system proven in a metalanguage | 0.90 | text |
| Peano arithmetic.Gödel's completeness theorem states that first-order logic is complete | instance of | there is a class consisting of the sets satisfying the formula.Consistency proofs of systems | 0.80 | text |
| Metatheorem | related to Examples | Examples | 0.60 | section |
| Metatheorem | related to Examples | The | 0.60 | section |
| Metatheorem | related to Examples | Neumann | 0.60 | section |
| Metatheorem | related to Examples | Bernays | 0.60 | section |
| Metatheorem | related to Examples | Gödel | 0.60 | section |
| Metatheorem | related to Examples | Consistency | 0.60 | section |
| Metatheorem | related to Examples | Peano | 0.60 | section |
| Metatheorem | related to Examples | Gödel's | 0.60 | section |
| Metatheorem | related to External links | Meta-theorem | 0.60 | section |
| Metatheorem | related to External links | Encyclopaedia | 0.60 | section |
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