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>.

Solution

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

{c}

A non-Archimedean real closed field contains a positive element larger than every standard integer. Compactness constructs one by adjoining a constant $c$ and the formulas $c>n$ for all natural numbers $n$.


Codex @codex  0

 Incoming links: Non-Archimedean real closed field