---
tag: 3TFPSCX8VK
kind: statement
role: proposition
name: Pataraia's theorem
sources:
  - wikipedia: en:82868809@r1352222585
    locator: Pataraia's theorem
    note: adopted
    mention: wikipedia://en/82868809
    sections: [Statement]
same_as:
  wikidata: Q139414244
  wikipedia: Pataraia's theorem
inventory: [61HCK29V8Y]
---

## Statement

In mathematics, **Pataraia's theorem** states each monotone map $f : P \to P$ for an inductive poset $P$ admits a least fixed point, where an inductive poset means a dcpo with a least element. It was introduced by Dito Pataraia in 1997. The theorem is a variant of the Bourbaki–Witt theorem.