|
In the mathematical field of set theory, the Solovay model is a model constructed by in which all of the axioms of Zermelo–Fraenkel set theory (ZF) hold, exclusive of the axiom of choice, but in which all sets of real numbers are Lebesgue measurable. The construction relies on the existence of an inaccessible cardinal. In this way Solovay showed that the axiom of choice is essential to the proof of the existence of a non-measurable set, at least granted that the existence of an inaccessible cardinal is consistent with ZFC, the axioms of Zermelo–Fraenkel set theory including the axiom of choice. ==Statement== ZF stands for Zermelo–Fraenkel set theory, and DC for the axiom of dependent choice. Solovay's theorem is as follows. Assuming the existence of an inaccessible cardinal, there is an inner model of ZF + DC of a suitable forcing extension ''V''() such that every set of reals is Lebesgue measurable, has the perfect set property, and has the Baire property. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Solovay model」の詳細全文を読む スポンサード リンク
|