Hypothesis: HR 165:
\(C(WO,WO)\): Every well ordered family of non-empty, well orderable sets has a choice function.
Conclusion: HR 105:
There is a partially ordered set \((A,\le)\) such that for no set \(B\) is \((B,\le)\) (the ordering on \(B\) is the usual injective cardinal ordering) isomorphic to \((A,\le)\).
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M11\) Forti/Honsell Model | Using a model of \(ZF + V = L\) for the ground model, the authors construct a generic extension, \(\cal M\), using Easton forcing which adds \(\kappa\) generic subsets to each regular cardinal \(\kappa\) |
Code: 3
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