Hypothesis: HR 204:
For every infinite \(X\), there is a function from \(X\) onto \(2X\).
Conclusion: HR 88:
\(C(\infty ,2)\): Every family of pairs has a choice function.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M2\) Feferman's model | Add a denumerable number of generic reals to the base model, but do not collect them |
| \(\cal N9\) Halpern/Howard Model | \(A\) is a set of atoms with the structureof the set \( \{s : s:\omega\longrightarrow\omega \wedge (\exists n)(\forall j > n)(s_j = 0)\}\) |
Code: 3
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