Hypothesis: HR 128:
Aczel's Realization Principle: On every infinite set there is a Hausdorff topology with an infinite set of non-isolated points.
Conclusion: HR 289:
If \(S\) is a set of subsets of a countable set and \(S\) is closed under chain unions, then \(S\) has a \(\subseteq\)-maximal element.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M1\) Cohen's original model | Add a denumerable number of generic reals (subsets of \(\omega\)), \(a_1\), \(a_2\), \(\cdots\), along with the set \(b\) containing them |
Code: 3
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