# 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. - published version (11p)

Bib entry

@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}, doi = {10.1007/s00153-003-0208-9}, mrclass = {03E40 (03E65)}, mrnumber = {2052883}, mrreviewer = {Miroslav Repick\'y}, doi = {10.1007/s00153-003-0208-9}, note = {\href{https://arxiv.org/abs/math/0112286}{arXiv: math/0112286}}, arxiv_number = {math/0112286} }