Hypothesis: HR 93:
There is a non-measurable subset of \({\Bbb R}\).
Conclusion: HR 142:
\(\neg PB\): There is a set of reals without the property of Baire. Jech [1973b], p. 7.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M18\) Shelah's Model I | Shelah modified Solovay's model, <a href="/models/Solovay-1">\(\cal M5\)</a>, and constructed a model without using an inaccessible cardinal in which the <strong>Principle of Dependent Choices</strong> (<a href="/form-classes/howard-rubin-43">Form 43</a>) is true and every set of reals has the property of Baire (<a href="/form-classes/howard-rubin-142">Form142</a> is false) |
Code: 3
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