Kleene’s fixed point theorem theorem constructs least fixed points of endofunctions on posets by iterating them. Adámek's fixed point theorem generalizes this to constructing initial algebras.
Let be a monotone function on a poset . If has a least element and joins of increasing sequences, and if preserves joins of increasing sequences, then a least fixed point of can be constructed as the join of the increasing sequence:
Named after Stephen Kleene.
See also:
Last revised on November 29, 2023 at 16:41:41. See the history of this page for a list of all contributions to it.