 The strongly inaccessible cardinal is necessary for the perfect set property (even for Π̰11 sets (Solovay)) and Lebesgue measurability (Shelah) but not for the property of Baire (Shelah). However, Martin and Solovay showed in 1970 that if ZFC is consistent then so is ZFC along with the statement that all Σ12 sets have the property of Baire and are Lebesgue measurable. 