The <Diagonal lemma> states that for every formula $\theta(x)$ with one free variable there is a sentence $\gamma$ such that
$$
PA^-\vdash\gamma\leftrightarrow\theta(\ulcorner\gamma\urcorner).
$$
The same conclusion holds in every theory extending the arithmetic needed to formalize substitution.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 120 / 2 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-120/2/b/solution