Form equivalence class Howard-Rubin Number: 14
Statement: (Depends on \(k\in\omega\), \(k\ge 2\)) \(P(k)\):If \(X\) is a set and \(P\) is a property of subsets of \(X\) of finite character(that is, \(\forall y\subseteq X (P(y)\) iff \(\forall z\subseteq y (z\)finite \(\rightarrow P(z)))\)), then if every finite subset of \(X\) can bepartitioned into \(k\) or fewer \(P\)-sets (that is,sets \(z\) such that \(P(z))\), then \(X\) can be partitioned into\(k\) or fewer \(P\)-sets. Cowen [1982].
Howard-Rubin number: 14 AD
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