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cf., Sent.I.D21.Q1.A2, Matt.C11.L3.n965
In this article, St. Thomas gives us four options for how we can interpret the combination of a person term (e.g., Father) with an exclusive term (i.e., "alone").
In the first sense, it can be taken as a categorematic term, i.e., "there is absolutely nobody else besides the Father in any category whatsoever." In this sense, it is clearly false, not only on account of the other Divine Persons, but also on account of creation.
On the other hand, it can also be taken as a syncategormatic term.