Can I say : We are not in a kindergarden. Should I say : We are not in kindergarden. Does usage of 'a' refer to a bulding?
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Exactly as you noted, in this case, the use of article refers to a building.
Saying "we're not in a kindergarten" you're expressing the fact that you're not in the building itself, while saying "we're not in kindergarten" generally says you don't attend kindergarten anymore.
Another example would be:
If your monthly PTA meeting takes place in a Kindergarten, you can say: "Please, people, we're adults. We're not in kindergarten anymore."
But you cannot say: "Please, people, we're adults. We're not in a kindergarten anymore." ... Because you are still in a kindergarten.
Obviously, your confusion seems to arise from the incorrect choice of an example (an example!).
Would that make the same difference as in the above example? No. The use of some article or the absence of it always makes the same difference of stating the definite, the indefinite and the general. I do not know if any infrastructure factors are involved at all.