Part (a) says that every partial embedding preserves every formula. By the characterization supplied in the question, each formula is therefore equivalent modulo $T_{\mathrm{rg}}$ to a quantifier-free formula. Hence the <quantifier elimination for the random graph> holds.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 144 / 2 / b / Solution

 Solution (source code)