Is a list automatically a plural construct? A visiting professor (native German speaker) has gotten into an argument with his coauthor over the following phrasing:
“There (is/are) a field K, an element k in K, a group G, a…”
All of the terms in the list are singular, and there seems to be no natural way to collect them into one singular object.
So, should ‘is’ or ‘are’ be used?
You’d use the singular, because the list is essentially replacing the repeating “there is.” For example: “There is a book, and there is a cat, and there is a dog, and there is a tape measure, and there is a Northumberlandian prostitute” becomes “There is a book, a cat, a dog, and a Northumberlandian prostitute.”
There might be more to it than that, but that’s the way I see it.
That sounds wrong to me (and not just because of ‘northumberlandian’ 
). I’d definitely use ‘are’, because there’s no collective category.
You could just use the backwards capital E, and avoid the question of singularity or plurality entirely :D.
I say use ‘is’: You are treating the group of objects as one entity, therefore it’s a singular.
“There is a dog, a cat, and a rat.” is to me essentially the same as “There is a row of houses.” or “There is a finite field.”
But you’d say “a dog, a cat, and a rat **are **there.” What’s the difference?
The difference lies in whether you are thinking of them individually or as a group.
The term in English for this is collective noun, although group noun is also used. The usual meaning of the term is for individual words that could be used both ways, as in team, committee or staff.
The staff are planning a surprise party for their boss.
The staff is going to a retreat on Friday.
Lists can be thought of in the same way. If you want to emphasize the individual nature of the items on the list you use a plural verb; if you want to empress them as a single totality you use a singular verb.
Al thought the distinction can be subtle, it’s all up to the intent of the author.
Darn spell checker:
Although the distinction can be subtle, it’s all up to the intent of the author.
I’m with the mapcase. It’s not math, it’s communication: use what is clearest and simplest to convey your idea to your audience. A typical English reader won’t be surprised or annoyed or otherwise have to take extra time to understand the sentence if you use ‘is’ there, and neither will it detract from the main idea if you use ‘are’ there. So you can use either, and you should use the one that best conveys your idea – if your idea is about the group aspect, use ‘is’; if it’s about the individual items, use ‘are’. Though I don’t think it’s a big deal either way.
[“The staff is highly trained for this situation.” “The staff are fighting over who gets the window office.” Or "There is a washer, dryer and a sink in the basement. " “There are a dog, a cat, a mouse, a ferret, an iguana, and a surly teenager, all of which need to be fed.”]
Although you’re accurate on the (grammatical) number of collectives here, my impression has always been that American (but not British!) usage has been to regard a collective as always singular unless it “rubs your nose” in its factual pluralness:
“The staff is going on a retreat.”
“The staff is planning a surprise party.” (British usage would call for your “are” here)
But “The Ways and Means Committee were so violently divided over the bill that one Senator threw a punch at another.”
From The Careful Writer, by Theodore Bernstein (using examples that had appeared in The New York Times where he was head copyeditor):
He goes on to say more or less what I said: think of the sense of the sentence and the impression that you want that sentence to convey. He uses oneness and more-than-oneness as the poles, which is what I said more elegantly. 
Here’s another example:
Bernstein was a conservative prescriptionist writing back in the 1960s. It seems to me that usage has gone even more away from Americans deferring to the singular since then.
But he’s not only talking about a field, but a field, an element, a group, and so on.
Do it this way … replace the “is/are” choice with the “exists/exist” choice. In a math proof, I’ll go with “exist” because I’d say “A field K, an element k in K, a group G, and … exist …”. So I’d go with “are”.
Yeah, wasn’t there also a priest and a bartender? 
Actually, I think it was a Rabbi! ;j