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 2M 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 |
|---|---|
| Canonical name | InductivelyOrdered |
| Date of creation | 2013-03-22 14:55:21 |
| Last modified on | 2013-03-22 14:55:21 |
| Owner | rspuzio (6075) |
| Last modified by | rspuzio (6075) |
| Numerical id | 8 |
| Author | rspuzio (6075) |
| Entry type | Definition |
| Classification | msc 06A99 |
| Related topic | ZornsLemma |
| Defines | inductive order |
| Defines | inductively orderes set |