---
tag: J0Z2GNJZ2W
kind: concept
name: Beta-model
sources:
  - wikipedia: en:72003155@r1349708555
    locator: Beta-model
    note: adopted
    mention: wikipedia://en/72003155
    sections: [Summary]
same_as:
  wikidata: Q114901462
  wikipedia: Beta-model
inventory: [3VZR3CSYKY]
---

## Summary

In model theory, a mathematical discipline, a **β-model** (from the French "bon ordre", well-ordering) is a model that is correct about statements of the form "*X* is well-ordered". The term was introduced by Mostowski (1959) as a strengthening of the notion of ω-model. In contrast to the notation for set-theoretic properties named by [[ordinals|0RDJK7EQYY]], such as $\xi$-indescribability, the letter β here is only denotational.