Maximal extension in a set

Set

context $A$ … set
context $a\in A$
definiendum $\mathrm{max}(a,A)\equiv\bigcup\{b\mid b\in A\land a\subseteq b\}$

Discussion

Idea

Given $a\in A$, the maximal extension $\mathrm{max}(a,A)$ is the largest set in $A$ which encompasses $a$.

Predicate

predicate $x$ maximal in $X \equiv \mathrm{max}(x,X)=x$

Reference

Parents

Element of

Set universe