Omega-complete partial order

Summary

An omega-complete partial order, or $\omega$-cpo, is a partially ordered set in which every increasing sequence has a supremum. It is a weaker form of a directed-complete partial order that is enough for the fixed-point semantics of recursive programs. Let the $\omega$-cpo have a least element $\bot$. Then a monotone map that preserves suprema of increasing sequences has a least fixed point, the supremum of its iterates on $\bot$.