Form equivalence class Howard-Rubin Number: 10
Statement: Assume \((P,\le)\) is a partial order such that \(P\)is a denumerable union of finite sets and contains a non-empty subset\(Q\) relative to which depths are defined for all \(x\in \) P. If all\(Q\)-strong antichains of \(P\) are finite then for each denumerablefamily \({\Cal D}\) of dense sets there is a \({\Cal D}\) generic filter.Shannon [1990] and Note 47.
Howard-Rubin number: 10 I
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