KnowraCategorical theoryLinked fromLinked fromThe 6 pages that link to Categorical theory, each with the reason it gives.All 6Related 1Compared with 5Model 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.Second-order logicRelated: Full second-order axioms can characterize structures categorically.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.