Kleene fixed-point theorem

• Kleene's fixed-point theorem

Named after American mathematician Stephen Cole Kleene.

the Kleene fixed-point theorem

1. (mathematics) Suppose ${\displaystyle (L,\sqsubseteq )}$ is a directed-complete partial order with a least element, and let ${\displaystyle f:L\to L}$ be a Scott-continuous (and therefore monotone) function. Then ${\displaystyle f}$ has a least fixed point, which is the supremum of the ascending Kleene chain of ${\displaystyle f}$.