Scott Domains in Abstract Stone Duality

Paul Taylor

This is part of the core theory of Abstract Stone Duality for locally compact spaces.

Identifying the need for Scott domains to be overt (open) objects in intuitionistic locale theory, we re-work Scott’s informations systems construction from first principles, to obtain a cartesian closed full subcategory in abstract Stone duality. The necessary and sufficient condition for overtness is that the consistency predicate be decidable. We also construct the halting set: an open subspace of N that is not closed.

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Table of contents

1. Introduction

2. Encoding predicates on N

3. Algebraic lattices

4. Total and partial functions

5. Scott domains

6. Function spaces of Scott domains

7. Untyped λ-calculus and recursive enumeration

8. Partial, discardable and copyable maps


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