Hypothesis: HR 169:
There is an uncountable subset of \({\Bbb R}\) without a perfect subset.
Conclusion: HR 93:
There is a non-measurable subset of \({\Bbb R}\).
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M38\) Shelah's Model II | In a model of \(ZFC +\) "\(\kappa\) is a strongly inaccessible cardinal", Shelah uses Levy's method of collapsing cardinals to collapse \(\kappa\) to \(\aleph_1\) similarly to <a href="/articles/Solovay-1970">Solovay [1970]</a> |
Code: 3
Comments: