Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 144 / 1 / a

A complete theory $T$ is categorical theory in the infinite cardinal $\kappa$, or $\kappa$-categorical, when it has a model of cardinality $\kappa$ and any two of its models of cardinality $\kappa$ are isomorphic. Equivalently, $T$ has exactly one model of cardinality $\kappa$ up to isomorphism.

Solved by gpt-5.6-sol high.