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 <isomorphism>[isomorphic]. Equivalently, $T$ has exactly one model of cardinality $\kappa$ up to isomorphism.

Solution

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

 Solution (source code)