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# inductively ordered

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

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

Cf. inductive set.

Defines:

inductive order, inductively orderes set

Related:

ZornsLemma

Major Section:

Reference

Type of Math Object:

Definition

Parent:

## Mathematics Subject Classification

06A99*no label found*

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