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Maximal extension in a set
Set
| context | $X$ … set |
| context | $a\in X$ |
| definiendum | $\mathrm{max}(a,A)$ |
| postulate | $\mathrm{max}(a,A)\in X$ |
| postulate | $a\subseteq\mathrm{max}(a,A)$ |
| forall | $b\in X$ |
| postulate | $a\subseteq b\implies b\subseteq \mathrm{max}(a,A)$ |
Discussion
todo: write this down order theoretical (define it in terms of an ordering defined via $\subseteq$)
Idea
Given $a\in X$, the maximal extension $a'$ is the largest amongs $X$ which does contain $a$.
Predicate
| predicate | $x$ maximal in $X \equiv \mathrm{max}(x,A)=x$ |
Reference
Parents
Element of
