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extendible cardinal
In mathematics, extendible cardinals are large cardinals introduced by , who was partly motivated by reflection principles. Intuitively, such a cardinal represents a point beyond which initial pieces of the universe of sets start to look similar, in the sense that each is elementarily embeddable into a later one.
==Definition==
For every ordinal ''η'', a cardinal κ is called η-extendible if for some ordinal ''λ'' there is a nontrivial elementary embedding ''j'' of ''V''κ+η into ''V''λ, where ''κ'' is the critical point of ''j'', and as usual ''Vα'' denotes the ''α''th level of the von Neumann hierarchy. A cardinal ''κ'' is called an extendible cardinal if it is ''η''-extendible for every ordinal ''η'' (Kanamori 2003).
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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