2 CARDINAL VERSIONS OF DIAMOND

Roughly speaking, lozenge(kappa,lambda) asserts the existence of a seq uence of size < kappa sets that captures every subset of lambda on a s tationary set. The paper is devoted to the study of lozenge(kappa,lamb da) and related principles, which are for instance obtained by conside ring sequences of larger sets, or by requesting the simultaneous captu re of many subsets of lambda. Our main result is that lozenge(kappa,la mbda) holds in case lambda > 2(<kappa).