Kleene fixed-point theorem

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English

English Wikipedia has an article on:

Kleene fixed-point theorem

Alternative forms

Kleene's fixed-point theorem

Etymology

Named after American mathematician Stephen Cole Kleene.

Proper noun

the Kleene fixed-point theorem

(mathematics) Suppose $(L,\sqsubseteq )$ is a directed-complete partial order with a least element, and let $f:L\to L$ 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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