A Universal Innocent Game Model for the Böhm Tree Lambda Theory

Andrew D. Ker, Hanno Nickau, C.-H. Luke Ong

Abstract: We present a game model of the untyped λ-calculus, with equational theory equal to the Böhm tree λ-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. Webuild 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 λ-calculus