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"The type of an object determines the set of values (that) it can have."

In the above sentence, which noun is modified by the relative clause "(that) it can have"?

a.) The noun "set" of the noun phrase "the set"

b.) The noun "values" of the prepositional phrase "of values"

  • It's almost redundant to use 'the set of values it can have'; 'the values it can have' has the same meaning. I acknowledge that the phrase is idiomatic and has the pragmatic effect of underlining that you're talking about all the possible values. But I'd not consider 'that it can have' to be modifying 'set' any more than 'all' in 'all the possible values that it can have'. – Edwin Ashworth Mar 17 '18 at 16:08
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    In constructions like this, the relative clause is normally seen as modifying the noun that is complement of the preposition "of". On that basis, the relative clause is modifying "values" not "set". – BillJ Mar 17 '18 at 16:20
  • BillJ Thank you very much for your simple and clear answer. – Sinushyperbolikus Mar 17 '18 at 16:23
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    Encouraged by your name, I'll give an answer based on mathematics rather than on English semantics.The phrase "that it can have" modifies "values", because values, not sets, are the sort of thing an object can have. Even if one says that an object can have such-and-such set of values, it means that the object can have each of the values in the set. – Andreas Blass Jul 16 '18 at 0:29
  • @Andreas But is "that" a relative pronoun or a conjunction (introducing a noun clause) in the sentence ? What if the sentence were, "The type of an object determines the set of values that provides a solution." There "that" is clearly a relative pronoun. In that sentence would it modify "set" or "values"? – Zan700 Sep 14 '18 at 2:13
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It can have values. It can have a set of values. I think the relative clause can be said to modify the noun "values" or the whole noun phrase "set of values"

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    "Set of values" is a noun phrase. – BillJ Mar 17 '18 at 16:21

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