Form equivalence class Howard-Rubin Number: 14
Statement: Let \(X\) be a set and \({\Cal D}=\{Y_{i}: i\in I\}\) afamily of finite pairwise disjoint subsets of \({\Cal P}(X)\).Suppose for every finite subset \(\{a, b,\ldots, k\}\) of \(I\),\(\exists s\in I\) such that \(Y_{s}\subseteq Y_{a}\land Y_{b}\land \ldots\land Y_{k}\) (If \(Y\) and \(Z\) are finite pairwise disjoint sets then\(Y\land Z = \{A\cap B: A\in Y\) and \(B\in Z\) and\(A\cap B\neq\emptyset\}\).) Then there is a choice function \(\mu\) whosedomain includes \({\Cal D}\) such that the family \(\{\mu(Y_{i}): i\in I\}\)(where \(\mu(Y_{i})\in Y_{i})\) of subsets of \(X\) is closed under finiteintersections. Rav [1977].
Howard-Rubin number: 14 AK
Citations (articles):
Connections (notes):
References (books):
Back