Form Classes

Form equivalence class Howard-Rubin Number: 270

Statement:

\(F^{\mathrm{fin}}_n\) (\(n\ge 3\) a natural number): For any family \({\cal F}\) of pairwise disjoint, \(n\) element sets if \(R\) is a symmetric binary relation on \(\bigcup {\cal F}\) which satisfies

  1. the set \(\{ b\in \bigcup {\cal F} : \neg a\mathrel R b\}\) is finite for every \(a \in \bigcup {\cal F}\), and
  2. every finite subfamily of \({\cal F}\) has an \(R\)-consistent choice function,
then \({\cal F}\) has an \(R\)-consistent choice function.

Howard-Rubin number: 270 C-n

Citations (articles): Kolany [1992] Equivalents of the compactness theorem for locally finite sets of sentences

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