Hypothesis: HR 219:
\((\forall n\in\omega-\{0\}) MC(\infty,WO\), relatively prime to \(n\)): For all non-zero \(n\in \omega\), if \(X\) is a set of non-empty well orderable sets, then there is a function \(f\) such that for all \(x\in X\), \(f(x)\) is a non-empty, finite subset of \(x\), and \(|f(x)|\) is relatively prime to \(n\).
Conclusion: HR 10:
\(C(\aleph_{0},< \aleph_{0})\): Every denumerable family of non-empty finite sets has a choice function.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|
Code: 3
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