A universal innocent game model for the Böhm tree lambda theory.

Abstract

We present a game model of the untyped lambda-calculus, with equational theory equal to the Böhm tree lambda-theory B, which is universal (i.e. every element of the model is definable by some term). This answers a question of Di Gianantonio, Franco and Honsell. We build on our earlier work, which uses the methods of innocent game semantics to develop a universal model inducing the maximal consistent sensible theory H^*. To our knowledge these are the first syntax-independent universal models of the untyped lambda-calculus.