Hypothesis: HR 92:
\(C(WO,{\Bbb R})\): Every well ordered family of non-empty subsets of \({\Bbb R}\) has a choice function.
Conclusion: HR 308-p:
If \(p\) is a prime and if \(\{G_y: y\in Y\}\) is a set of finite groups, then the weak direct product \(\prod_{y\in Y}G_y\) has a maximal \(p\)-subgroup.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N6\) Levy's Model I | \(A=\{a_n : n\in\omega\}\) and \(A = \bigcup \{P_n: n\in\omega\}\), where \(P_0 = \{a_0\}\), \(P_1 = \{a_1,a_2\}\), \(P_2 =\{a_3,a_4,a_5\}\), \(P_3 = \{a_6,a_7,a_8,a_9,a_{10}\}\), \(\cdots\); in generalfor \(n>0\), \(|P_n| = p_n\), where \(p_n\) is the \(n\)th prime |
Code: 3
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