Frink Ideal - Basic Definitions

Basic Definitions

LU(A) is the set of all lower bounds of the set of all 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 P, S I implies that LU(S) I.

A subset I of a partially ordered set (P,≤) is a normal ideal or a cut if LU(I) I.

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