Hypothesis: HR 9:
Finite \(\Leftrightarrow\) Dedekind finite: \(W_{\aleph_{0}}\) Jech [1973b]: \(E(I,IV)\) Howard/Yorke [1989]): Every Dedekind finite set is finite.
Conclusion: HR 380:
\(PC(\infty,WO,\infty)\): For every infinite family of non-empty well orderable sets, there is an infinite subfamily \(Y\) of \(X\) which has a choice function.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N49\) De la Cruz/Di Prisco Model | Let \(A = \{ a(i,p) : i\in\omega\land p\in {\Bbb Q}/{\Bbb Z} \}\) |
Code: 3
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