- Extendible cardinal
In
mathematics , acardinal number κ is η-extendible if and only if for some λ there is a nontrivialelementary embedding j of:"V"κ+η
into
:"V"λ
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 aresupercompact cardinal s.ee also
*
List of large cardinal properties 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
*
Wikimedia Foundation. 2010.
