### Forcing axiom failure for any $\lambda > \aleph_1$

by Shelah. [Sh:784]

Archive for Math Logic, 2004

David Aspero asks on the possibility of having Forcing axiom
FA_{{aleph_2}}(K), where K is the class of
forcing notions preserving stationarily of subsets of aleph_1 and
of aleph_2 . We answer negatively, in fact we show the negative
result for any regular lambda > aleph_1 even demanding adding no
new sequence of ordinals of length < lambda .

Back to the list of publications