Form equivalence class Howard-Rubin Number:
99
Statement:
Strong Rado Lemma 2: Let \(T\) be a family of finite
sets and let \({\cal F}\) be a collection of finite subsets of \(T\)
satisfying
- \((\forall K\in T)(\exists S\in {\cal F})(K\in S)\)
- \((\forall S_{1}, S_{2}\in{\cal F})(S_{1}\cup S_{2}\in {\cal F})\)
Assume there is a function \(\phi\) with domain \({\cal F}\) such that for each \(S\in{\cal F}\), \(\phi(S) = \phi_{S}\) is a function with domain \(S\) and satisfies \((\forall K\in S)(\phi_{S}(K)\in K)\). Then there is
a function \(f\) with domain \(T\) and with the following property: For all
\(S\in{\cal F}\) there is an \(S'\in{\cal F}\) such that \(S\subseteq S'\) and
\(f\) and \(\phi_{S'}\) agree on \(S\).
Howard-Rubin number:
99 C
Citations (articles):
Howard [1993]
Variations of Rado's lemma
Connections (notes):
References (books):
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