Form Classes

Form equivalence class Howard-Rubin Number: 270

Statement:

\(F_{\mathrm{fin}}\): For any family \({\cal F}\) of pairwise disjoint, non-empty, finite 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 B

Citations (articles): Kolany/Wojtylak [1991] Restricted versions of the compactness theorem

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