Form equivalence class Howard-Rubin Number: 14
Statement: Engler's Lemma: Let \({\Cal E}\) be a family offunctions whose domains are subsets of a set \(S\) with range \(\subseteq\{0,1\}\) and such that\itemitem{(a)} For every finite \(F\subseteq S\), \(\exists \phi \in {\Cal E}\)with domain F.\itemitem{(b)} The restriction of any function in \({\Cal E}\) to any subsetof its domain is in \({\Cal E}\).\itemitem{(c)}If \(\phi \) is any function with domain \(\phi\subseteq S\) suchthat the restriction of \(\phi \) to any finite subset of its domain is in\({\Cal E}\) then \(\phi \in {\Cal E}\).\item{} Then \(\exists f\in {\Cal E}\) whose domain is \(S\).Rav [1977].
Howard-Rubin number: 14 AI
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