Adapting innocent game models for the Böhm treelambda -theory

We present a game model of the untyped λ-calculus, with equational theory equal to the Bohm 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. 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 λ-calculus.

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