Form equivalence class Howard-Rubin Number: 14

Statement:  Disjoint Transversal axiom (2,3):  If \(X\) is a  set,\({\Cal U}\) is a subset of \(\{y\subseteq X : | y|\le 2\}\) and \({\Cal V}\)is a subset of \(\{y\subseteq X: | y|\le 3\}\) and if for each two finitesubsets \({\Cal U}_{0}\subseteq{\Cal U}\) and \({\Cal V}_{0}\subseteq{\Cal V}\)there are transversals \(Y_{1}\) and \(Y_{2}\) for \({\Cal U}_{0}\)  and\({\Cal V}_{0}\) respectively such that \(Y_{1}\cap Y_{2}=\emptyset\), thenthere are  disjoint transversals \(X_{1}\) and \(X_{2}\) for \({\Cal U}\) and\({\Cal V}\) respectively. (\(Y\subseteq X\) is a transversal for \({\Cal U}\)if for all \(y\in{\Cal U}\), \(y\cap Y\neq\emptyset\).)  Schrijver [1978].

Howard-Rubin number: 14 AF

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