---
tag: J2C8EAM521
kind: concept
name: Categorical
sources:
  - wikipedia: en:43580500@r1360947732
    locator: Glossary of set theory, section C
    note: adopted
    mention: wikipedia://en/43580500#VF98
    sections: [Summary]
inventory: [C9RRZCWKC7]
---

## Summary

A theory is called categorical if all models are isomorphic. This definition is no longer used much, as first-order theories with infinite models are never categorical.

A theory is called k-categorical if all models of cardinality *κ* are isomorphic