The <Stone prime filter theorem> says that if a <lattice filter> $F$ and a <lattice ideal> $I$ of a <distributive lattice> are disjoint, then there is a <prime filter of a distributive lattice> $P$ such that
$$
F\subseteq P
\quad\text{and}\quad
P\cap I=\varnothing.
$$
Equivalently, whenever $a\nleq b$, there is a prime filter containing $a$ and omitting $b$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 120 / 3 / c / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-120/3/c/solution