Two categories of effective continuous cpos

Authors:
G. Hamrin;V. Stoltenberg-Hansen
Affiliations:
Department of Mathematics, Uppsala University, Uppsala, Sweden;Department of Mathematics, Uppsala University, Uppsala, Sweden
Venue:
Theoretical Computer Science - Spatial representation: Discrete vs. continous computational models
Year:
2006

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Abstract

This paper presents two categories of effective continuous complete partial orders (cpos). We define a new criterion on the basis of a cpo so as to make the resulting category of consistently complete continuous cpos cartesian closed. We also generalise to continuous cpos the definition of a complete set, which was used as a definition of effective bifinite domains in Hamrin and Stoltenberg-Hansen [Cartesian closed categories of effective domains, in: H. Schwichtenberg, R. Steinbrüggen (Eds.), Proof and System-Reliability, Kluwer Academic Publishers, Dordrecht, 2002, pp. 1-20], and investigate the closure results that can be obtained.