Two cardinal versions of diamond (Q690039)

Roughly speaking, \(\diamondsuit_{\kappa,\lambda}\) asserts the existence of a sequence of size \(<\kappa\) sets that capture every subset of \(\lambda\) on a stationary set. The paper is devoted to the study of \(\diamondsuit_{\kappa, \lambda}\) and related principles, which are for instance obtained by considering sequences of larger sets, or by requesting the simultaneous capture of many subsets of \(\lambda\). Our main result is that \(\diamondsuit_{\kappa, \lambda}\) holds in case \(\lambda> 2^{< \kappa}\).