Martin's maximum
From Wikipedia, the free encyclopedia
In set theory, Martin's maximum, introduced by Foreman, Magidor & Shelah (1988), is a generalization of the proper forcing axiom, which is in turn a generalization of Martin's axiom.
Martin's maximum states that if D is a collection of ℵ1 dense subsets of a stationary set preserving notion of forcing then there is a D-generic filter.
The existence of a supercompact cardinal implies the consistency of Martin's maximum.
[edit] References
- Foreman, M.; Magidor, M. & Shelah, S. (1988), “Martin's maximum, saturated ideals, and nonregular ultrafilters. I.”, Ann. of Math. 127 (1): 1-47, MR0924672, <http://links.jstor.org/sici?sici=0003-486X%28198801%292%3A127%3A1%3C1%3AMMSIAN%3E2.0.CO%3B2-U> correction
- Jech, Thomas (2003), Set Theory: Millennium Edition, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag, ISBN 978-3-540-44085-7
