# 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 (http://planetmath.org/Set); any finite set of integers is inductively ordered by divisibility.

Cf. inductive set.

Title inductively ordered InductivelyOrdered 2013-03-22 14:55:21 2013-03-22 14:55:21 rspuzio (6075) rspuzio (6075) 8 rspuzio (6075) Definition msc 06A99 ZornsLemma inductive order inductively orderes set