Form equivalence class Howard-Rubin Number: 14
Statement: Monteiro's Theorem for Complete Atomic BooleanAlgebras: Let \(K\) be a complete atomic Boolean algebra,\(A\) a subalgebra of the Boolean algebra \(B\) and \(f\) a homomorphism from\(A\) to \(K\). Let \(d\) be a semimorphism from \(B\) into \(K\) (that is, \(d :B \to K,\ d(0) = 0,\ d(1) = 1\) and for all \(x, y\in B\), \(d(x \lory) = d(x) \lor d(y)\) ) with \(f(x) \le d(x)\) for all \(x \in A\). Thenthere is a homomorphism \(h\) from \(B\) to \(K\) such that \(h(x) \le d(x)\)for all \(x \in B\) and \(h/A = f\). Monteiro [1965] and Bacsich [1972a].
Howard-Rubin number: 14 BA
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