Order Theory and Fixed Points in Posets

This group gathers theorems about partially ordered sets and the fixed points of order-preserving or inflationary maps on them, a part of the foundations of mathematics that supplies tools to set theory, logic, and theoretical computer science. It covers the Bourbaki-Witt theorem, a basic fixed-point theorem for partially ordered sets that are chain complete, and Pataraia's theorem, which gives a least fixed point for every monotone map on an inductive poset and is a variant of the Bourbaki-Witt theorem. Such results give routes to fixed points that avoid the heavier machinery of Zorn's lemma and transfinite recursion, and they underlie the semantics of recursive definitions. Fixed-point theorems for continuous maps on topological spaces belong with Topology instead.