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 .

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