Constructive set theoretic models of typed combinatory logic

Journal of Symbolic Logic 58 (1):99-118 (1993)
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 simple typed combinatory logic is the theory of a full function space model
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