Hypothesis: HR 144:
Every set is almost well orderable.
Conclusion: HR 51:
Cofinality Principle: Every linear ordering has a cofinal sub well ordering. Sierpi\'nski [1918], p 117.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N37\) A variation of Blass' model, \(\cal N28\) | Let \(A=\{a_{i,j}:i\in\omega, j\in\Bbb Z\}\) |
| \(\cal N41\) Another variation of \(\cal N3\) | \(A=\bigcup\{B_n; n\in\omega\}\)is a disjoint union, where each \(B_n\) is denumerable and ordered like therationals by \(\le_n\) |
Code: 5
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