Hypothesis: HR 181:
\(C(2^{\aleph_0},\infty)\): Every set \(X\) of non-empty sets such that \(|X|=2^{\aleph_0}\) has a choice function.
Conclusion: HR 203:
\(C\)(disjoint,\(\subseteq\Bbb R)\): Every partition of \({\cal P}(\omega)\) into non-empty subsets has a choice function.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M2(\langle\omega_2\rangle)\) Feferman/Truss Model | This is another extension of <a href="/models/Feferman-1">\(\cal M2\)</a> |
Code: 3
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