Kleene fixed-point theorem

English

Alternative forms

• Kleene's fixed-point theorem

Etymology

Named after American mathematician Stephen Cole Kleene.

Proper noun

the Kleene fixed-point theorem

1. (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 $f$.