Invariance of interpretation by beta-conversion is one of the minimal requirements for any standard model for the gimel-calculus. With the intersection-type systems being a general framework for the study of semantic domains for the gimel-calculus, the present paper provides a (syntactic) characterisation of the above mentioned requirement in terms of characterisation results for intersection-type assignment systems. Instead of considering conversion as a whole, reduction and expansion will be considered separately. Not only for usual computational rules like beta, eta, but also for a number of relevant restrictions of those. Characterisations will be also provided for (intersection) filter structures that are indeed gimel-models. (c) 2006 Elsevier B.V. All rights reserved.
