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- Kleene_fixed-point_theorem abstract "In the mathematical areas of order and lattice theory, the Kleene fixed-point theorem, named after American mathematician Stephen Cole Kleene, states the following:Let L be a complete partial order, and let f : L → L be a Scott-continuous (and therefore monotone) function. Then f has a least fixed point, which is the supremum of the ascending Kleene chain of f.The ascending Kleene chain of f is the chainobtained by iterating f on the least element ⊥ of L. Expressed in a formula, the theorem states thatwhere denotes the least fixed point.This result is often attributed to Alfred Tarski, but Tarski's fixed point theorem pertains to monotone functions on complete lattices.".
- Kleene_fixed-point_theorem wikiPageID "1234125".
- Kleene_fixed-point_theorem wikiPageRevisionID "578036294".
- Kleene_fixed-point_theorem hasPhotoCollection Kleene_fixed-point_theorem.
- Kleene_fixed-point_theorem subject Category:Fixed-point_theorems.
- Kleene_fixed-point_theorem subject Category:Order_theory.
- Kleene_fixed-point_theorem type Abstraction100002137.
- Kleene_fixed-point_theorem type Communication100033020.
- Kleene_fixed-point_theorem type Fixed-pointTheorems.
- Kleene_fixed-point_theorem type Message106598915.
- Kleene_fixed-point_theorem type Proposition106750804.
- Kleene_fixed-point_theorem type Statement106722453.
- Kleene_fixed-point_theorem type Theorem106752293.
- Kleene_fixed-point_theorem type TheoremsInDiscreteMathematics.
- Kleene_fixed-point_theorem comment "In the mathematical areas of order and lattice theory, the Kleene fixed-point theorem, named after American mathematician Stephen Cole Kleene, states the following:Let L be a complete partial order, and let f : L → L be a Scott-continuous (and therefore monotone) function. Then f has a least fixed point, which is the supremum of the ascending Kleene chain of f.The ascending Kleene chain of f is the chainobtained by iterating f on the least element ⊥ of L.".
- Kleene_fixed-point_theorem label "Kleene fixed-point theorem".
- Kleene_fixed-point_theorem label "Théorème du point fixe de Kleene".
- Kleene_fixed-point_theorem label "克莱尼不动点定理".
- Kleene_fixed-point_theorem sameAs Théorème_du_point_fixe_de_Kleene.
- Kleene_fixed-point_theorem sameAs m.04krbn.
- Kleene_fixed-point_theorem sameAs Q3527263.
- Kleene_fixed-point_theorem sameAs Q3527263.
- Kleene_fixed-point_theorem sameAs Kleene_fixed-point_theorem.
- Kleene_fixed-point_theorem wasDerivedFrom Kleene_fixed-point_theorem?oldid=578036294.
- Kleene_fixed-point_theorem isPrimaryTopicOf Kleene_fixed-point_theorem.