| context | $A$ … set |
| context | $a\in A$ |
| definiendum | $\mathrm{max}(a,A)\equiv\bigcup\{b\mid b\in A\land a\subseteq b\}$ |
Given $a\in A$, the maximal extension $\mathrm{max}(a,A)$ is the largest set in $A$ which encompasses $a$.
| predicate | $x$ maximal in $X \equiv \mathrm{max}(x,X)=x$ |