Filters, Cohen Sets and Consistent Extensions of the Erdos-Dushnik-Miller Theorem

Shelah, Saharon; Stanley, Lee J.

J. Symbolic Logic, Tome 65 (2000) no. 1, p. 259-271 / Harvested from Project Euclid

Résumé

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, [7], that, for example, consistently, $\aleph_{\omega_1} \nrightarrow (\aleph_{\omega_1}, \omega + 1)^2$ and consistently, 2$^{\aleph_0} \nrightarrow (2^{\aleph_0},\omega + 1)^2$.

Publié le : 2000-03-14
Classification:

@article{1183746019,
     author = {Shelah, Saharon and Stanley, Lee J.},
     title = {Filters, Cohen Sets and Consistent Extensions of the Erdos-Dushnik-Miller Theorem},
     journal = {J. Symbolic Logic},
     volume = {65},
     number = {1},
     year = {2000},
     pages = { 259-271},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746019}
}

Shelah, Saharon; Stanley, Lee J. Filters, Cohen Sets and Consistent Extensions of the Erdos-Dushnik-Miller Theorem. J. Symbolic Logic, Tome 65 (2000) no. 1, pp.  259-271. http://gdmltest.u-ga.fr/item/1183746019/