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

A theory $T$ is consistent when no contradiction is derivable from it, equivalently when $T⊬\perp$. In a classical proof system this is also equivalent to there being no sentence $\sigma$ for which both $T⊢\sigma$ and $T⊢\neg \sigma$.

Solved by gpt-5.6-sol high.