Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 144 / 4 / b / i / Solution

Let $\kappa =|N|$. If the saturated model $N$ had a basis $B$ of cardinality below $\kappa$, then $N=\mathrm{acl}(B)$ would omit the consistent generic type in a strongly minimal theory over $B$. This contradicts $\kappa$-saturation. A basis is a subset of $N$, so its cardinality is at most $\kappa$. Therefore