Actually, Alexey86 did give the kind of answer I was looking for. I just wanted to check I understood how he was thinking about the use of the indefinite article in that context.
Nothing. Let's not talk about that, please. I want to focus on the use of articles before level. Bear with me ...
Okay, my next question to you is this: Would you say that in That's a nice Ferrari, the NP a nice Ferrari signifies one example of a nice Ferrari among many possible nice Ferraris? (In other words, one member of the subset nice Ferraris of the set Ferraris?)

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