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


Solution

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

 Solution (source code)