Sh:804

• Matet, P., & Shelah, S. Positive partition relations for P_\kappa(\lambda). Preprint. arXiv: math/0407440
• Abstract:
  Let \kappa a regular uncountable cardinal and \lambda a cardinal >\kappa, and suppose \lambda^{<\kappa} is less than the covering number for category {\rm cov}({\mathcal M}_{\kappa, \kappa}). Then

  (a) I_{\kappa,\lambda}^+\mathop{\longrightarrow}\limits^\kappa (I_{\kappa,\lambda}^+,\omega+1)^2,

  (b) I_{\kappa,\lambda}^+\mathop{\longrightarrow}\limits^\kappa [I_{\kappa,\lambda}^+]_{\kappa^+}^2 if \kappa is a limit cardinal, and

  (c) I_{\kappa,\lambda}^+ \mathop{\longrightarrow}\limits^\kappa (I_{\kappa,\lambda}^+)^2 if \kappa is weakly compact.

• Version 2004-07-06_10 (26p)

@article{Sh:804,
 author = {Matet, Pierre and Shelah, Saharon},
 title = {{Positive partition relations for $P_\kappa(\lambda)$}},
 note = {\href{https://arxiv.org/abs/math/0407440}{arXiv: math/0407440}},
 arxiv_number = {math/0407440}
}