Two cardinal versions of diamond. (English) Zbl 0798.03047

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 \(\lambda> 2^{< \kappa}\).
Reviewer: P.Matet (Caen)


03E05 Other combinatorial set theory
03E35 Consistency and independence results
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