Sh:784

• Shelah, S. (2004). Forcing axiom failure for any $\lambda>\aleph_1$. Arch. Math. Logic, 43(3), 285–295. arXiv: math/0112286 DOI: 10.1007/s00153-003-0208-9 MR: 2052883
• Abstract:
  David Aspero asks on the possibility of having Forcing axiom $FA_{{\aleph_2}}(\mathfrak{K})$, where $\mathfrak{K}$ 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 $<\lambda$.
• Version 2004-03-01_10 (16p) published version (11p)

@article{Sh:784,
 author = {Shelah, Saharon},
 title = {{Forcing axiom failure for any $\lambda>\aleph_1$}},
 journal = {Arch. Math. Logic},
 fjournal = {Archive for Mathematical Logic},
 volume = {43},
 number = {3},
 year = {2004},
 pages = {285--295},
 issn = {0933-5846},
 mrnumber = {2052883},
 mrclass = {03E40 (03E65)},
 doi = {10.1007/s00153-003-0208-9},
 note = {\href{https://arxiv.org/abs/math/0112286}{arXiv: math/0112286}},
 arxiv_number = {math/0112286}
}