Form equivalence class Howard-Rubin Number: 14
Statement: (Depends on \(k\), \(n\in\omega\) with \(k\ge 2\), \(n\ge 2\)and \(n + k\ge 5\).) \(P(k,n)\): If \(X\) is a set and \(P\) is a property ofsubsets of \(X\) of \(n\) character (that is, \(\forall y\subseteq X (P(y)\)iff \(\forall z\subseteq y (|z|\le n\rightarrow P(z))))\), then if everyfinite subset of \(X\) can be partitioned into \(k\) or fewer \(P\)-sets(that is, sets \(z\) such that \(P(z)\)) then \(X\) can be partitionedinto \(k\) or fewer \(P\)-sets. Cowen [1982].
Howard-Rubin number: 14 AC
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