Form equivalence class Howard-Rubin Number: 201
Statement:
Disjoint Transversal axiom (2,2): If \(X\) is a set and \({\cal U}\) and \({\cal V}\) are subsets of \(\{ y\subseteq X : |y|\le 2\}\) and if for each two finite subsets \({\cal U}_{0}\subseteq {\cal U}\) 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 \(Y_{1} \cap Y_{2} = \emptyset\), then there 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 \(y\in \cal U\), \(y\cap Y \ne\emptyset\).)
Howard-Rubin number: 201 B
Citations (articles):
Schrijver [1978]
The dependence of some logical axioms on disjoint transversals and linked systems
Connections (notes):
References (books):
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