---
tag: WDNCGJAEWN
kind: concept
name: Prewellordering
aliases: [norm-descriptive-set-theory, prewellordering-property, reduction-property, regular-norm]
sources:
  - wikipedia: en:2137523@r1273597295
    locator: Prewellordering
    note: adopted
    mention: wikipedia://en/2137523
    sections: [Summary]
same_as:
  wikidata: Q7242444
  wikipedia: Prewellordering
inventory: [76CWJD54R7]
---

## Summary

In set theory, a **prewellordering** on a [[set|0BSJ7RQ9BW]] $X$ is a [[preorder|0VABYWJWH9]] $\leq$ on $X$ (a [[transitive|0CYRECG2YQ]] and [[reflexive|0X8NMST0J2]] relation on $X$) that is strongly connected (meaning that any two points are comparable) and [[well-founded|0230ECX1Q5]] in the sense that the induced relation $x < y$ defined by $x \leq y \text{ and } y \nleq x$ is a [[well-founded relation|0230ECX1Q5]].