(2005), we assume that final scope determination requires two elements: formulae with epsilon terms like (9) and scope statements in the form of Scope(S<x<y), where S is interpreted as some temporal index.
(Abusch, 1993) Sentence (3) allows the intermediate scope reading, meaning that, for every professor x, there is a certain book y such that for every student z, x rewarded z who read y on x's reading list, in which some book takes scope over the preceding universally quantified expression every student in the matrix clause but still co-varies along with the choice of professor.