Cofinal set

2010 Mathematics Subject Classification: Primary: 06A [MSN][ZBL]

in a partially ordered set $(A,{<})$

A subset $B$ of $(A,{<})$ with the property that for every $a \in A$ there is $b \in B$ such that $a \le b$. Dually, a co-initial set $B$ has the property that for every $a \in A$ there is $b \in B$ such that $b \le a$.

References

• R. Fraïssé, Theory of Relations, Studies in Logic and the Foundations of Mathematics, Elsevier (2011) p.44. ISBN 0080960413