Two categories of effective continuous cpos

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.