Am I understanding this sentence by Tolkien correctly?
Solution 1:
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Yes, it does, and you can in an informal context like this.
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V. for very is a v. common abbreviation, kn. much less so (but he has written it out in full in the previous clause).
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"I have a Dutch dictionary [which is] very much better [than the Swedish dictionary I used]."
This is evidently an informal letter to someone he knows well.