---
tag: A22K1X8GKD
kind: concept
name: Omega-categorical theory
aliases: [countably-categorical-theory, omega-categorical, omega-categorical-theories, omega-categoricity, categorical, categorical-theory, categoricity]
sources:
  - wikipedia: en:26628083@r1299172324
    locator: Omega-categorical theory
    note: adopted
    mention: wikipedia://en/26628083
    sections: [Summary]
same_as:
  wikidata: Q7089964
  wikipedia: Omega-categorical theory
inventory: [1FGM3P0KN0]
---

## Summary

In mathematical logic, an **omega-categorical theory** is a theory that has exactly one [[countably infinite|01TQB88H4C]] model up to isomorphism. Omega-categoricity is the special case κ = $\aleph_0$ = ω of κ-categoricity, and omega-categorical theories are also referred to as **ω-categorical**. The notion is most important for countable [[first-order|086QKPF0A6]] theories.