Effectively given domains and lambda-calculus models
Information and Control
Type theories, normal forms, and D∞-lambda-models
Information and Computation
Full abstraction for sequential algorithms: the state of the art
Algebraic methods in semantics
Lambda-calculus, types and models
Lambda-calculus, types and models
Set-theoretical and other elementary models of the &lgr;-calculus
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Journal of Computer and System Sciences
Mathematical theory of domains
Mathematical theory of domains
Information and Computation
PCF extended with real numbers
Theoretical Computer Science - Special issue on real numbers and computers
Domains and lambda-calculi
Theoretical Computer Science - Modern algebra and its applications
Uncountable limits and the lambda calculus
Nordic Journal of Computing
Stable Models of Typed lambda-Calculi
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
Extensional Embedding of a Strongly Stable Model of PCF
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
Topological incompleteness and order incompleteness of the lambda calculus
ACM Transactions on Computational Logic (TOCL)
Order-Incompleteness and Finite Lambda Models, Extended Abstract
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Order-incompleteness and finite Lambda reduction models
Theoretical Computer Science
βη-complete models for System F
Mathematical Structures in Computer Science
The Sensible Graph Theories of Lambda Calculus
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
The Lattice of Lambda Theories
Journal of Logic and Computation
Graph models of $\lambda$-calculus at work, and variations
Mathematical Structures in Computer Science
Theoretical Computer Science - Algebraic methods in language processing
Boolean Algebras for Lambda Calculus
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Fundamenta Informaticae - Typed Lambda Calculi and Applications (TLCA'99)
Lambda theories of effective lambda models
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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A longstanding open problem is whether there exists a non-syntactical model of the untyped λ-calculus whose theory is exactly the least λ-theory λβ. In this paper we investigate the more general question of whether the equational/order theory of a model of the untyped λ-calculus can be recursively enumerable (r.e. for short). We introduce a notion of effective model of λ-calculus, which covers, in particular, all the models individually introduced in the literature. We prove that the order theory of an effective model is never r.e.; from this it follows that its equational theory cannot be λβ or λβη. We then show that no effective model living in the stable or strongly stable semantics has an r.e. equational theory. For Scott's semantics, we investigate the class of graph models and prove that no order theory of a graph model can be r.e., and that there exists an effective graph model whose equational/order theory is the minimum among the theories of graph models. Finally, we show that the class of graph models enjoys a kind of downwards Löwenheim–Skolem theorem.