The family is a <nondecreasing family of sets> when
$$
A_s\subseteq A_t\qquad(0\leq s\leq t).
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 203 / 1 / c / i / Solution

A family of sets $(A_t)$ indexed by an <partially ordered set> is nondecreasing when
$$
s\leq t\quad\Longrightarrow\quad A_s\subseteq A_t.
$$