Form equivalence class Howard-Rubin Number: 14
Statement: Topological Rado Lemma: Let \(\{T_i: i\in I\}\)be a family of compact Hausdorff spaces and suppose for each finite\(F\subseteq I\), there is a set \(\Phi(F)\) of partial choice functionson \(I\) whose domains include \(F\) and such that (a) \(F_1\subseteq F_2\)implies \(\Phi(F_2)\subseteq\Phi(F_{1})\) and (b) the set\(\{\phi\vert F: \phi\in\Phi(F)\}\) is closed in \(\prod\{T_i: i\in F\}\) inthe product topology. Then there is a choice function \(f\) on \(I\)satisfying for any finite \(F\subseteq I\), \(\exists\phi\in\Phi(F)\) suchthat \(f\) and \(\phi\) coincide on \(F\). Rav [1977].
Howard-Rubin number: 14 AG
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