Can a lambda-model have a recursively enumerable theory ?

Chantal Berline (1)

1 PPS - Preuves, Programmes et Systèmes

Each model of the untyped λ-calculus (λ-model) induces an equational theory over λ-terms and the study and the classification of these theories is a rich and difficult subject. Most of the known proper (= non syntactical) λ-models are ordered structures. The following long standing open question was raised by Honsell in 1984: "Does there exist a proper λ-model whose equational theory is exactly the least equational theory λ_{β} " ; and similarly for λ_{βη}, the least extensional equational theory. We adress the still more general question of whether the equational/order theory of a proper λ-model can be recursively enumerable and conjecture that the answer is "No" for all the models living in Scott's.continuous semantics or one of its refinements (e.g. the stable or the strongly stable semantics) and give a survey of all the partial results we obtained.

Domaines: Logique [math.LO]

Chantal Berline. Can a lambda-model have a recursively enumerable theory ?. Types and Computations: A Colloquium in Honor of Mario Coppo, Mariangiola Dezani-Ciancaglini, Simona Ronchi della Rocca, Oct 2007, Roma, Italy. ⟨hal-00699810⟩