I'm asking about whether or not this phrase is grammatically correct: 'children 12 and under'.
I am also asking for a general analysis of constructions of this type.
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Yes, it is correct. This is a type of construction where a plural or indefinite noun has a "range" modifier. When I think of examples, some of them allow of to be inserted before the modifier, others don't.
See the comment below on the parallel with this and the types of sentences said in early generative grammar to be formed by "whiz deletion".
Yes if "12" is implicitly understood to mean "who are 12 years old" (and if "are 12 years old" is implicitly understood to mean "have reached the 12th anniversary of their birth but have not yet reached the 13th anniversary"). "Under 12" then implies "younger than 12 years old".
No if you think this is not clearly implied or understood.
I would go with the former.