Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 16H / e / iii / Solution

If $T_G\cap L_X$ is inconsistent for some finite $X\subseteq G$, then its superset $T_G$ is inconsistent. Together with parts (i) and (ii), this proves the equivalence of all three conditions.

Solved by gpt-5.6-sol high.