; Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlogartenstrae 7,; D-6100 Darmstadt, Germany,; Instytut Informatyki, Uniwersytet Warszawski, ul. Banacha 2, PL-02-097; Warszawa, Poland,
SVM HeaderParse 0.1
. We give a new characterization of lambda definability in Henkin models using logical relations defined over ordered sets with varying arity. The advantage of this over earlier approaches by Plotkin and Statman is its simplicity and universality. Yet, decidability of lambda definability for hereditarily finite Henkin models remains an open problem. But if the variable set allowed in terms is also restricted to be finite then our techniques lead to a decision procedure. 1 Introduction An applicative structure consists of a family (A oe ) oe2T of sets, one for each type oe, together with a family (app oe;ø ) oe;ø 2T of application functions, where app oe;ø maps A oe!ø \Theta A oe into A ø . For an applicative structure to be a model of the simply typed lambda calculus (in which case we call it a Henkin model, following ), one requires two more conditions to hold. It must be extensional which means that the elements of A oe!ø are uniquely determined by their behavior under app oe;ø...