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.

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Meanings

proper nounthe Kleene fixed-point theorem

alternative Kleene's fixed-point theorem

  1. mathematicsSuppose (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.

Origin

Named after American mathematician Stephen Cole Kleene.

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Cite this entry
APA

Kleene fixed-point theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/Kleene%20fixed-point%20theorem

MLA

“Kleene fixed-point theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Kleene%20fixed-point%20theorem. Accessed November 2, 2026.

Chicago

WatkinsX Dictionary, s.v. “Kleene fixed-point theorem,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/Kleene%20fixed-point%20theorem.

Source: Kleene fixed-point theorem on Wiktionary, CC BY-SA 4.0.