The word each, when attached to a noun phrase as in the sentence ``The kids bought three books each.'', has a number of unusual syntactic and semantic properties. It operates on two different noun phrases in the sentence; the Dist phrase, to which each attaches, must be numeric and indefinite, while the other noun phrase---the Range---may be definite or indefinite so long as it is plural. The Relation between those two noun phrases need not be a transitive verb; nearly any two-place relation will do. In this thesis I analyse this situation and develop a theory that accounts for these observations. In so doing, I use this ``binominal each'' construction to argue for the basic correctness of certain pre-existing linguistic theories, and for a few specific modifications thereto.
@mastersthesis{blah03,
author = {Don Blaheta},
title = {Binominal \emph{each}: evidence for a modified type system},
school = {Brown University},
year = 2003}