Abstract.
Coherence-spaces and domains with totality are used to give interpretations of inductively defined types. A category of coherence spaces with totality is defined and the closure of positive inductive type constructors is analysed within this category. Type streams are introduced as a generalisation of types defined by strictly positive inductive definition. A semantical analysis of type streams with continuous recursion theorems is established. A hierarchy of domains with totality defined by positive induction is defined, and density for a sub-hierarchy is proved.
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Received March 27, 1995
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Kristiansen, L., Normann, D. Total objects in inductively defined types. Arch Math Logic 36, 405–436 (1997). https://doi.org/10.1007/s001530050073
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DOI: https://doi.org/10.1007/s001530050073