Form equivalence class Howard-Rubin Number: 14
Statement: Principle of Consistent Choices: Let \(\{T_i:i\in I\}\) be a family of compact Hausdorf spaces and suppose \(R\) is asymmetric binary relation defined for all pairs of elements belongingto distinct \(T_i\) and such that for all \(i\neq j\) in \(I\), the set\(E(i,j)=\{(x,y): x\mathrel R y\) and \(x\in T_i\) and \(y\in T_j\}\) isclosed in \(T_i\times T_j\). Furthermore suppose that for every finitesubset \(F\subseteq I\), with at least two elements, \(\exists\phi\in\prod\{T_i:i\in F\}\) such that \(\phi(i)\mathrel R\phi(j)\) for all \(i\neq j\)in \(F\). Then \(\exists f\in\prod\{T_i: i\in I\}\) such that \(f(i)\mathrelR f(j)\) for all \(i\neq j\) in \(I\). Rav [1977].
Howard-Rubin number: 14 AH
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