In this paper, the authors investigate the semantics of the indefinite determiner eyze in Modern Hebrew, which is referred to as 'existential eyze'. This determiner can optionally appear in indefinite NPs, and, superficially, its presence seems not to affect the truth conditions of a sentence. It is argued, however, that the determiner does make a semantic contribution. Sentences are provided in which its occurrence clearly affects truth conditions. Further, the authors discuss the relation between this determiner and the wh-item eyze (which), which is found in interrogative clauses. They propose a formal semantic analysis of both interrogative and existential eyze that is formulated within the framework of Alternative Semantics. Under this analysis, both types of eyze trigger an 'alternative' interpretation of the expression to which they apply; however, only existential eyze further contributes an existential operator that ranges over the members of the set of alternatives.