---
tag: F855E3QA4B
kind: statement
role: proposition
name: Chang's conjecture
aliases: [chang-conjecture]
sources:
  - wikipedia: en:25403351@r1333249759
    locator: Chang's conjecture
    note: adopted
    mention: wikipedia://en/25403351
    sections: [Statement]
same_as:
  wikidata: Q5071569
  wikipedia: Chang's conjecture
inventory: [VGQXWQRW3A]
---

## Statement

In model theory, a branch of mathematical logic, **Chang's conjecture**, attributed to Chen Chung Chang by (Vaught 1963, 309), states that every model of type (ω<sub>2</sub>,ω<sub>1</sub>) for a countable language has an elementary submodel of type (ω<sub>1</sub>,ω). A model is of type (*α*,*β*) if it is of cardinality *α* and a unary relation is represented by a subset of cardinality *β*. The usual notation is $(\omega_2,\omega_1)\twoheadrightarrow(\omega_1,\omega)$.