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- Herbrand's_theorem abstract "Herbrand's theorem is a fundamental result of mathematical logic obtained by Jacques Herbrand (1930). It essentially allows a certain kind of reduction of first-order logic to propositional logic. Although Herbrand originally proved his theorem for arbitrary formulas of first-order logic, the simpler version shown here, restricted to formulas in prenex form containing only existential quantifiers became more popular.Let be a formula of first-order logic with quantifier-free. Then is valid if and only if there exists a finite sequence of terms: , with and , such that is valid. If it is valid, is called a Herbrand disjunction for Informally: a formula in prenex form containing existential quantifiers only is provable (valid) in first-order logic if and only if a disjunction composed of substitution instances of the quantifier-free subformula of is a tautology (propositionally derivable).The restriction to formulas in prenex form containing only existential quantifiers does not limit the generality of the theorem, because formulas can be converted to prenex form and their universal quantifiers can be removed by Herbrandization. Conversion to prenex form can be avoided, if structural Herbrandization is performed. Herbrandization can be avoided by imposing additional restrictions on the variable dependencies allowed in the Herbrand disjunction.".
- Herbrand's_theorem wikiPageExternalLink herbrandtheorem.
- Herbrand's_theorem wikiPageID "2518328".
- Herbrand's_theorem wikiPageRevisionID "542408662".
- Herbrand's_theorem hasPhotoCollection Herbrand's_theorem.
- Herbrand's_theorem subject Category:Metatheorems.
- Herbrand's_theorem subject Category:Proof_theory.
- Herbrand's_theorem subject Category:Theorems_in_the_foundations_of_mathematics.
- Herbrand's_theorem type Abstraction100002137.
- Herbrand's_theorem type Communication100033020.
- Herbrand's_theorem type Message106598915.
- Herbrand's_theorem type Proposition106750804.
- Herbrand's_theorem type Statement106722453.
- Herbrand's_theorem type Theorem106752293.
- Herbrand's_theorem type TheoremsInTheFoundationsOfMathematics.
- Herbrand's_theorem comment "Herbrand's theorem is a fundamental result of mathematical logic obtained by Jacques Herbrand (1930). It essentially allows a certain kind of reduction of first-order logic to propositional logic. Although Herbrand originally proved his theorem for arbitrary formulas of first-order logic, the simpler version shown here, restricted to formulas in prenex form containing only existential quantifiers became more popular.Let be a formula of first-order logic with quantifier-free.".
- Herbrand's_theorem label "Herbrand's theorem".
- Herbrand's_theorem label "Satz von Herbrand".
- Herbrand's_theorem label "Teorema de Herbrand".
- Herbrand's_theorem label "Théorème de Herbrand".
- Herbrand's_theorem label "Twierdzenie Herbranda".
- Herbrand's_theorem label "エルブランの定理".
- Herbrand's_theorem label "埃尔布朗定理".
- Herbrand's_theorem sameAs Satz_von_Herbrand.
- Herbrand's_theorem sameAs Théorème_de_Herbrand.
- Herbrand's_theorem sameAs エルブランの定理.
- Herbrand's_theorem sameAs Twierdzenie_Herbranda.
- Herbrand's_theorem sameAs Teorema_de_Herbrand.
- Herbrand's_theorem sameAs m.07kf4p.
- Herbrand's_theorem sameAs Q1930577.
- Herbrand's_theorem sameAs Q1930577.
- Herbrand's_theorem sameAs Herbrand's_theorem.
- Herbrand's_theorem wasDerivedFrom Herbrand's_theorem?oldid=542408662.
- Herbrand's_theorem isPrimaryTopicOf Herbrand's_theorem.