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In mathematical set theory, a cumulative hierarchy is a family of sets ''W''α indexed by ordinals α such that *''W''α⊆''W''α+1 *If α is a limit then ''W''α = ∪β<α ''W''β It is also sometimes assumed that ''W''α+1⊆''P''(''W''α) or that ''W''0 is empty. The union ''W'' of the sets of a cumulative hierarchy is often used as a model of set theory. The phrase "the cumulative hierarchy" usually refers to the standard cumulative hierarchy ''V''α of the Von Neumann universe with ''V''α+1=''P''(''V''α). ==Reflection principle== A cumulative hierarchy satisfies a form of the reflection principle: any formula of the language of set theory that holds in the union ''W'' of the hierarchy also holds in some stages ''W''α. 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「Cumulative hierarchy」の詳細全文を読む スポンサード リンク
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