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Gimel function : ウィキペディア英語版 | Gimel function In axiomatic set theory, the gimel function is the following function mapping cardinal numbers to cardinal numbers: : where cf denotes the cofinality function; the gimel function is used for studying the continuum function and the cardinal exponentiation function. The symbol is a serif form of the Hebrew letter gimel. ==Values of the Gimel function==
The gimel function has the property for all infinite cardinals κ by König's theorem. For regular cardinals , , and Easton's theorem says we don't know much about the values of this function. For singular , upper bounds for can be found from Shelah's PCF theory.
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「Gimel function」の詳細全文を読む
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