NDLI: Extensional Σ-Spaces in Type Theory

Content Provider	Springer Nature Link
Author	Reus, Bernhard
Copyright Year	1999
Abstract	Synthetic Domain Theory provides a setting for denotational semantics following Dana Scott's slogan ‘domains as sets’ in which all functions are continuous. Several approaches can be found in the literature, but they are either model-dependent or if they use an axiomatic setting then not uniformly and not explicitly. We present a completely logical approach to Synthetic Domain Theory (SDT), axiomatizing (complete) Extensional PERs. On these grounds some basic domain theory is developed. Special attention is devoted to admissibility. The axiomatic approach is advantageous since it allows for easy formalization and comparison to other axiomatic settings.The consistency of the theory is shown by providing an appropriate realizability model. It is discussed how to get from this ‘special kind’ of SDT ‘{à la Scott}’ to a more general form which unifies several approaches.
Starting Page	159
Ending Page	183
Page Count	25
File Format	PDF
ISSN	09272852
Journal	Applied Categorical Structures
Volume Number	7
Issue Number	1-2
e-ISSN	15729095
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	1999-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theory of Computation Geometry Convex and Discrete Geometry Mathematical Logic and Foundations
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Algebra and Number Theory Computer Science

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Extensional Σ-Spaces in Type Theory