Sources
open directory project
Help build the largest human-edited directory on the web.
Submit a site - Become an editor
Wikipedia. Licensed under the GNU Free Documentation License.
Are you an expert in this subject? Join the discussion and share your knowledge at Wikipedia.org.
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.
"A cardinal κ is extendible if and only if for all α 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.
 |
This mathematical logic-related article is a stub. You can help Wikipedia by expanding it. |