Abstract
We study models of the untyped lambda calculus in the setting of game semantics. In particular, we show that, in the category of games G, introduced by Abramsky, Jagadeesan and Malacaria, all categorical α-models can be partitioned in three disjoint classes, and each model in a class induces the same theory (i.e. the set of equations between terms), that are the theory H., the theory which identifies two terms if they have the same Böhm tree and the theory which identifies all the terms which have the same Lévy-Longo tree.
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Gianantonio, P.D., Franco, G. (2000). The Fine Structure of Game Lambda Models. In: Kapoor, S., Prasad, S. (eds) FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2000. Lecture Notes in Computer Science, vol 1974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44450-5_35
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DOI: https://doi.org/10.1007/3-540-44450-5_35
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