# Sh:419

- Shelah, S., & Stanley, L. J. (2000).
*Filters, Cohen sets and consistent extensions of the Erdős-Dushnik-Miller theorem*. J. Symbolic Logic,**65**(1), 259–271. arXiv: math/9709228 DOI: 10.2307/2586535 MR: 1782118 -
Abstract:

We present two different types of models where, for certain singular cardinals \lambda of uncountable cofinality, \lambda\rightarrow(\lambda,\omega+1)^2, although \lambda is not a strong limit cardinal. We announce, here, and will present in a subsequent paper, that, for example, consistently, \aleph_{\omega_1}\not\rightarrow (\aleph_{\omega_1},\omega+1)^2 and consistently, 2^{\aleph_0}\not\rightarrow (2^{\aleph_0},\omega+1)^2. - published version (14p)

Bib entry

@article{Sh:419, author = {Shelah, Saharon and Stanley, Lee J.}, title = {{Filters, Cohen sets and consistent extensions of the Erd\H{o}s-Dushnik-Miller theorem}}, journal = {J. Symbolic Logic}, fjournal = {The Journal of Symbolic Logic}, volume = {65}, number = {1}, year = {2000}, pages = {259--271}, issn = {0022-4812}, mrnumber = {1782118}, mrclass = {03E02 (03E35)}, doi = {10.2307/2586535}, note = {\href{https://arxiv.org/abs/math/9709228}{arXiv: math/9709228}}, arxiv_number = {math/9709228} }