Greek polydefinites are cases of adjectival modification where the adjective features its own definite determiner. We propose an account of the phenomenon that treats it as an instance of close apposition. Like close appositives, polydefinites in Greek instantiate multiple definite determiners, display a freedom in word order, and involve a restrictive interpretation. We propose that close apposition in Greek forms a complex DP out of two DPs which are in a sisterhood relationship through identification of the Referential roles within the DPs. This operation, semantically tantamount to set intersection, is constrained to apply only when the resulting set is not co-extensive with either initial set. This ensures the restrictive interpretation of one DP over the other. The fact that in polydefinites, it is always the DP containing the adjective that obligatorily satisfies the constraint has to do with the presence of noun ellipsis within that DP: (noun) ellipsis is known to come with a disanaphora requirement. We show that noun ellipsis is also responsible for the distribution of adjectives and adjective interpretations, as well as those discourse effects of polydefinites that have been thought of as the result of a DP-internal Focus projection. Finally, we make a proposal for the encoding of definiteness in Greek, consonant both with the existence of polydefinites in the language and with the prerequisite for set intersection among DPs: the overtly realized Greek definite determiner does not itself contribute an iota operator but preserves the <e,t>denotation at the DP level. Our proposal thus deals not only with the multiple occurrence of definite determiners in a construction that picks out a single discourse referent, but also with the compositionality problem that such a situation gives rise to. In the final part we tie the cross-linguistic (un)availability of expletive determiners of the Greek type to the (un)availability of morphologically realized case.