Compare:
كِتَابُ زَيْدٍ - definite, because زَيْدٍ identifies a particular person.
كِتَابُ وَلَدٍ - indefinite but more specific than كِتَابٌ, because وَلَدٍ still means an unspecified boy.
The form of the mudaf ilayh decides whether the phrase becomes definite or merely more specific.
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Compare:
كِتَابُ زَيْدٍ - definite, because زَيْدٍ identifies a particular person.
كِتَابُ وَلَدٍ - indefinite but more specific than كِتَابٌ, because وَلَدٍ still means an unspecified boy.
The form of the mudaf ilayh decides whether the phrase becomes definite or merely more specific.