Description:
[62 E] implies Form 62
Content:
We give a proof of:
[62 E] (\(KW(\infty,<\aleph_0)\)) implies Form 62 (\(C(\infty,<\aleph_0)\)).
Let \(x\) be a set of finite sets and let \(y=\{u:(\exists v\in x)u\subseteq v\}\). By [62 E], there is a Kinna-Wagner selection function, \(f\), on \(y\). We define a choice function \(g\) on \(x\) as follows: Let \(u\in x\) be such that \(|u|=n\). There exists an \(m\in\omega\), \(m \lt n\), such that \(f^m(u)\) is a singleton. Define \(g(u)\) to be the single element of \(f^m(u)\). (Form 323, \(KW(WO,\infty)\), clearly implies [62 E].)
Howard-Rubin number:
70
Type:
Theorem
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