Linked from

The 6 pages that link to Categorical theory, each with the reason it gives.

• Model theoryCompared with: Categoricity contrasts with the many nonisomorphic models first-order theories can have.

• Compactness theoremCompared with: Compactness constrains categoricity across infinite cardinalities in countable first-order languages.

• Löwenheim–Skolem theoremCompared with: The theorem rules out categoricity across all infinite cardinalities for theories with infinite models.

• Elementary equivalenceCompared with: Categoricity can force equivalent models of that size to be structurally identical.

• Skolem's paradoxCompared with: First-order set theory lacks categoricity across infinite cardinalities, allowing models of varied sizes.