Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 144 / 3 / ii / Solution

Expand RCF by a constant $c$ and the sentences $c>n$ for all natural numbers $n$. Every finite subset is realized in $\mathbb{R}$. The compactness theorem gives a model realizing all of them, hence a Non-Archimedean real closed field.