Form equivalence class Howard-Rubin Number: 14
Statement: Almost Maximal Ideal Theorem: Every bounded,non-trivial, distributive lattice has an almost maximal ideal.(Definitions: If \(D\) is a bounded non-trivial distributivelattice, \(I(D)\) is the lattice of ideals of \(D\). An almost maximalideal in \(D\) is an ideal \(P\) of \(D\) such that \(s(P) = P\) where \(s\) isthe operation on \(I(D)\) defined as follows: If \(e\) is the unit of \(I(D)\),(i) For \(a\in I(D)\) we say \(x\in I(D)\) is \(a\)-small if \(x\vee b = e\)implies \(a\vee b = e\) for all \(b \in I(D)\). (ii) For any \(a\in I(D)\),\(s(a)\) is the join of all a-small elements of \(I(D)\)).Banaschewski/Harting [1985] and Blass [1986].
Howard-Rubin number: 14 E
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