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Constructive set theoretic models of typed combinatory logic

Published online by Cambridge University Press:  12 March 2014

Andreas Knobel
Andreas Knobel*
Affiliation:
Computer Language Section, Computer Science Division, Electrotechnical Laboratory, Tsukuba 305, Japan, E-mail: andreas@etl.go.jp
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Abstract

We shall present two novel ways of deriving simply typed combinatory models. These are of interest in a constructive setting. First we look at extension models, which are certain subalgebras of full function space models. Then we shall show how the space of singletons of a combinatory model can itself be made into one. The two and the algebras in between will have many common features. We use these two constructions in proving:

There is a model of constructive set theory in which every closed extensional theory of simply typed combinatory logic is the theory of a full function space model.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 1 , March 1993 , pp. 99 - 118
Copyright
Copyright © Association for Symbolic Logic 1993

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