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From The Cambridge Grammar of the English Language, page 519:
Genitives, such as Christ’s in [4iv], we take to be modifiers not determiners. They occur readily in names that are themselves functioning as modifier within a larger construction, as in a Christ’s College don: this is a construction which accepts nominals but not full NPs in modifier position. Such genitives cannot normally contain a determiner — compare King’s College, Women’s College, etc.
I don’t see what is the clear difference between modifiers and determiners. Aren’t the latter just included in the modifiers’ category?
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StoneyB gives a good definition in the second paragraph of their answer to this question.
– None – 2014-11-24T05:50:28.3603A single NP has only one available determiner slot. But, an NP can have zero to many modifier slots. Determinatives are in competition with each other to fill that one determiner slot. That is, "a" or "the" or "that" or "this" or etc. can fit that determiner slot, but only one of them can be used, e.g. "A this big red box is on sale" is ungrammatical because "A" competes with "this" for that one determiner slot. – F.E. – 2014-11-24T18:38:30.317
3Though, be aware that determinatives can also function as modifier in NP structure. That is, the determinative "five" is functioning as a determiner in "Five boys are at the door" , while it is functioning as a modifier in "These five lazy boys are your students". – F.E. – 2014-11-24T18:45:23.903