Hypothesis: HR 363:
There are exactly \(2^{\aleph_0}\) Borel sets in \(\Bbb R\). G. Moore [1982], p 325.
Conclusion: HR 337:
\(C(WO\), uniformly linearly ordered): If \(X\) is a well ordered collection of non-empty sets and there is a function \(f\) defined on \(X\) such that for every \(x\in X\), \(f(x)\) is a linear ordering of \(x\), then there is a choice function for \(X\).
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N53\) Good/Tree/Watson Model I | Let \(A=\bigcup \{Q_n:\ n\in\omega\}\), where \(Q_n=\{a_{n,q}:q\in \Bbb{Q}\}\) |
Code: 3
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