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[parent] inductively ordered (Definition)

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.



"inductively ordered" is owned by rspuzio. [ owner history (1) ]
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See Also: Zorn's lemma

Also defines:  inductive order, inductively orderes set

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Cross-references: inductive set, divisibility, integers, finite set, power set, upper bound, elements, chain, iff, partially ordered set
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This is version 5 of inductively ordered, born on 2005-01-02, modified 2005-04-14.
Object id is 6610, canonical name is InductivelyOrdered.
Accessed 3206 times total.

Classification:
AMS MSC: 06A99 (Order, lattices, ordered algebraic structures :: Ordered sets :: Miscellaneous)
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