## Paper: A Continuum of Theories of Lambda Calculus without Semantics (at LICS 2001)

**Antonino Salibra**

### Abstract

In this paper we give a topological proof of the following result: There exist 2^{\aleph_0} lambda theories of the untyped lambda calculus without a model in any semantics based on Scott's view of models as partially ordered sets and of functions as monotonic functions. As a consequence of this result, we positively solve the conjecture, stated by Bastonero-Gouy [6, 7] and by Berline [10], that the strongly stable semantics is incomplete.

### BibTeX

@InProceedings{Salibra-AContinuumofTheorie, author = {Antonino Salibra}, title = {A Continuum of Theories of Lambda Calculus without Semantics}, booktitle = {Proceedings of the Sixteenth Annual IEEE Symposium on Logic in Computer Science (LICS 2001)}, year = {2001}, month = {June}, pages = {334--343}, location = {Boston, MA, USA}, publisher = {IEEE Computer Society Press} }