In mathematics, a Frink ideal, introduced by Orrin Frink, is a certain kind of subset of a partially ordered set.
Basic definitions.
LU("A") is the set of all common lower bounds of the set of all common upper bounds of the subset "A" of a partially ordered set.
A subset "I" of a partially ordered set ("P", ≤) is a Frink ideal, if the following condition holds:
For every finite subset "S" of "I", we have LU("S") formula_1 "I".
A subset "I" of a partially ordered set ("P", ≤) is a normal ideal or a cut if LU("I") formula_1 "I".