A projective valuation oil a set E is a mapping w: E-4 --> Lambdaboolean OR{+/-infinity}, where Lambda is an ordered abelian group, satisfying certain axiorris. A D-relation on E is a four-place relation on E, again with certain properties. There is a projective valuation on the set of ends of a Lambda-tree (and on any subset, by restriction) and we show, using a construction suggested by Tits in the case Lambda = R, that every projective valuation arises in this way. Every projective valuation it, defines a D-relation, and there is a simple geometric interpretation of the D-relation, given a A-tree defining w. Our main result is a converse, that any D-relation can be defined by a projective valuation, hence arises from an embedding into the set of ends of a Lambda-tree. [References: 19]
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