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Kleene fixed-point theorem

Kleene fixed-point theorem proper noun: suppose (L,⊑) is a directed-complete partial order with a least element, 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.

Proper noun

the Kleene fixed-point theorem

  1. Suppose (L,⊑) is a directed-complete partial order with a least element, 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.

Forms of Kleene fixed-point theorem

alternative formKleene's fixed-point theorem

Origin of Kleene fixed-point theorem

Named after American mathematician Stephen Cole Kleene.

Questions about Kleene fixed-point theorem

What does Kleene fixed-point theorem mean?
Kleene fixed-point theorem means suppose (L,⊑) is a directed-complete partial order with a least element, 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.
What part of speech is Kleene fixed-point theorem?
Kleene fixed-point theorem is a proper noun.

Words near Kleene fixed-point theorem in the dictionary

  1. Kleene
  2. Kleene algebra
  3. Kleene algebras
  4. Kleene closure
  5. Kleene closures
  6. Kleene fixed-point theorem
  7. Kleene hierarchy
  8. Kleene operator
  9. Kleene operators
  10. Kleene plus
  11. Kleene pluses

Source and license

Adapted from Wiktionary: Kleene fixed-point theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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