Abstract

In this paper I compare two well studied approaches to topological semantics| the domain-theoretic approach, exemplied by the category of countably based equilogical spaces, Equ, and Type Two Eectivity, exemplied by the category of Baire space representations, Rep(B ). These two categories are both locally cartesian closed extensions of countably based T 0 -spaces. A natural question to ask is how they are related.

Citations

200	Introduction to Computable Analysis - Weihrauch - 2000
55	Realizability Toposes and Language Semantics - Longley - 1995
40	Mathematical Theory of Domains - Rijsbergen, Stoltenberg-Hansen, et al. - 1994
39	Countable functionals - Kleene - 1959
34	The Realizability Approach to Computable Analysis and Topology - Bauer
33	The foundations of intuitionistic mathematics, especially in relation to recursive functions - Kleene, Vesley - 1965
25	Handbook of Categorical Algebra I: Basic Category Theory - Borceux - 1994
24	Equilogical spaces - Bauer, Birkedal, et al. - 1998
21	Local realizability toposes and a modal logic for computability - Awodey, Birkedal, et al.
19	Theory of representations - Kreitz, Weihrauch - 1985
19	Topological and limit-space subcategories of countably-based equilogical spaces - Menni, Simpson
13	Type 2 recursion theory - Weihrauch - 1985
12	Continuous functionals of dependent types and equilogical spaces - Bauer, Birkedal - 2000
12	Total sets and objects in domain theory, Annals of Pure and Applied Logic 60 - Berger - 1993
9	Continuous Functionals of Dependent and Transitive Types. Habilitationsschrift, Ludwig-Maximilians-Universitat Munchen - Berger - 1997
8	Admissible representations of limit spaces - Schröder - 2000
6	Categories of domains with totality - Normann - 1997
6	Computability - Weihrauch - 1987
4	The largest topological subcategory of countablybased equilogical spaces - Simpson, Menni - 1999
3	Eectivity and density in domains: A survey - Berger - 2000
3	Computability on Topological Spaces by Eective Domain Representations - Blanck - 1997
2	A new category - Scott - 1996
1	Domains and Lambda-Calculi," Cambridge Tracts - Amadio, Curien - 1998
1	Sheaf toposes for realizability (2000), available at Bauer http://andrej.com/papers - Awodey, Bauer
1	Comparing realizability over P - Lietz - 1999
1	The continuous functionals of types over the reals, Preprint Series 19 - Normann - 1998