English

Positive partition relations for P_{kappa,lambda}

Logic 2007-05-23 v1

Abstract

Let kappa a regular uncountable cardinal and lambda a cardinal >kappa, and suppose lambda^{<kappa} is less than the covering number for category cov(M_{kappa,kappa}). Then (a) I_{kappa,lambda}^+ -->^kappa (I_{kappa, lambda}^+,omega +1)^2, (b) I_{kappa, lambda}^+ -->^kappa [I_{kappa, lambda}^+]_{kappa^+}^2 if kappa is a limit cardinal, and (c) I_{kappa, lambda}^+ -->^kappa (I_{kappa, lambda}^+)^2 if kappa is weakly compact.

Cite

@article{arxiv.math/0407440,
  title  = {Positive partition relations for P_{kappa,lambda}},
  author = {Pierre Matet and Saharon Shelah},
  journal= {arXiv preprint arXiv:math/0407440},
  year   = {2007}
}