Hypothesis: 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.
Conclusion: HR 390:
Every infinite set can be partitioned either into two infinite sets or infinitely many sets, each of which has at least two elements. Ash [1983].
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N1\) The Basic Fraenkel Model | The set of atoms, \(A\) is denumerable; \(\cal G\) is the group of all permutations on \(A\); and \(S\) isthe set of all finite subsets of \(A\) |
Code: 5
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