Form equivalence class Howard-Rubin Number: 50
Statement: For any complete Boolean algebra \(B\) and any subalgebra\(A\) of \(B\), there is a \(U \in V^{(B)}\) such that \(V^{(B)}\models\)``\(U\) is an ultrafilter on \(A\) and \(U^B \subseteq U\)''. (\(V^{(B)}\) isthe Boolean valued universe constructed from \(B\), \(U^B = \{ (\hat x,x)\, : x\in B\,\}\) is the canonical ultrafilter on \(B\) and \(x\mapsto\hat x\)is the canonical embedding of \(V\) into \(V^{(B)}\).) Bell [1977]and \cite{1983}.
Howard-Rubin number: 50 F
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