Hypothesis: HR 6:
\(UT(\aleph_0,\aleph_0,\aleph_0,\Bbb R)\): The union of a denumerable family of denumerable subsets of \({\Bbb R}\) is denumerable.
Conclusion: HR 293:
For all sets \(x\) and \(y\), if \(x\) can be linearly ordered and there is a mapping of \(x\) onto \(y\), then \(y\) can be linearly ordered.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N28\) Blass' Permutation Model | The set \(A=\{a^i_{\xi}: i\in \Bbb Z, \xi\in\aleph_1\}\) |
| \(\cal N37\) A variation of Blass' model, \(\cal N28\) | Let \(A=\{a_{i,j}:i\in\omega, j\in\Bbb Z\}\) |
Code: 3
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