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Abstract

Assuming that an inaccessible cardinal exists, we construct a ZFC-model where every Delta 1 4 -set is measurable but there exists a Delta 1 4 -set without the property of Baire. By a result of Shelah, an inaccessible cardinal is necessary for this result.
The author is partially supported by the Basic Research Foundation of the Israel Academy of Sciences and by the Swiss National Funds.

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