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inductively ordered

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A partially ordered set $A$ is {\em inductively ordered} iff every chain of elements of $A$ has an upper bound in $A$.

\textbf{Examples.} \,The power set $2^M$ of any set $M$ is inductively ordered by the \PMlinkname{set inclusion}{Set}; any finite set of integers is inductively ordered by divisibility.

Cf. inductive set.