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- Conservativity_theorem abstract "In mathematical logic, the conservativity theorem states the following: Suppose that a closed formula is a theorem of a first-order theory . Let be a theory obtained from by extending its language with new constants and adding a new axiom . Then is a conservative extension of , which means that the theory has the same set of theorems in the original language (i.e., without constants ) as the theory .In a more general setting, the conservativity theorem is formulated for extensions of a first-order theory by introducing a new functional symbol:Suppose that a closed formula is a theorem of a first-order theory , where we denote . Let be a theory obtained from by extending its language with new functional symbol (of arity ) and adding a new axiom . Then is a conservative extension of , i.e. the theories and prove the same theorems not involving the functional symbol ).".
- Conservativity_theorem wikiPageID "2101754".
- Conservativity_theorem wikiPageRevisionID "473474812".
- Conservativity_theorem hasPhotoCollection Conservativity_theorem.
- Conservativity_theorem subject Category:Mathematical_logic.
- Conservativity_theorem subject Category:Proof_theory.
- Conservativity_theorem subject Category:Theorems_in_the_foundations_of_mathematics.
- Conservativity_theorem type Abstraction100002137.
- Conservativity_theorem type Communication100033020.
- Conservativity_theorem type Message106598915.
- Conservativity_theorem type Proposition106750804.
- Conservativity_theorem type Statement106722453.
- Conservativity_theorem type Theorem106752293.
- Conservativity_theorem type TheoremsInTheFoundationsOfMathematics.
- Conservativity_theorem comment "In mathematical logic, the conservativity theorem states the following: Suppose that a closed formula is a theorem of a first-order theory . Let be a theory obtained from by extending its language with new constants and adding a new axiom .".
- Conservativity_theorem label "Conservativity theorem".
- Conservativity_theorem sameAs m.06m792.
- Conservativity_theorem sameAs Q5163116.
- Conservativity_theorem sameAs Q5163116.
- Conservativity_theorem sameAs Conservativity_theorem.
- Conservativity_theorem wasDerivedFrom Conservativity_theorem?oldid=473474812.
- Conservativity_theorem isPrimaryTopicOf Conservativity_theorem.