English

Ideals, Cohen sets and consistent extensions of the Erd\H{o}s-Dushnik-Miller Theorem

Logic 2016-09-07 v1

Abstract

We present two different types of models where, for certain singular cardinals lambda of uncountable cofinality, lambda -> (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-> (aleph_{omega_1}, omega+1)^2 and consistently, 2^{aleph_0} not-> (2^{aleph_0},omega +1)^2 .

Keywords

Cite

@article{arxiv.math/9709228,
  title  = {Ideals, Cohen sets and consistent extensions of the Erd\H{o}s-Dushnik-Miller Theorem},
  author = {Saharon Shelah and Lee Stanley},
  journal= {arXiv preprint arXiv:math/9709228},
  year   = {2016}
}