Extendible cardinal
From Wikipedia, the free encyclopedia
In mathematics, a cardinal number κ is η-extendible if and only if for some λ there is a nontrivial elementary embedding j of
- Vκ+η
into
- Vλ
where κ is the critical point of j.
κ is an extendible cardinal if and only if it is η-extendible for every ordinal number η.
Vopenka's principle implies the existence of extendible cardinals. All extendible cardinals are supercompact cardinals.
[edit] See also
[edit] References
"A cardinal κ is extendible if and only if for all α>κ there exists β and an elementary embedding from V(α) into V(β) with critical point κ." -- "Restrictions and Extensions" by Harvey M. Friedman http://www.math.ohio-state.edu/~friedman/pdf/ResExt021703.pdf
- Kanamori, Akihiro (2003). The Higher Infinite : Large Cardinals in Set Theory from Their Beginnings, 2nd ed, Springer. ISBN 3-540-00384-3.
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