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• W2058174669 abstract "Abstract The first example of a simultaneous inductive-recursive definition in intuitionistic type theory is Martin-Löfs universe à la Tarski. A set U 0 of codes for small sets is generated inductively at the same time as a function T 0 , which maps a code to the corresponding small set, is defined by recursion on the way the elements of U 0 are generated. In this paper we argue that there is an underlying general notion of simultaneous inductive-recursive definition which is implicit in Martin-Löf's intuitionistic type theory. We extend previously given schematic formulations of inductive definitions in type theory to encompass a general notion of simultaneous induction-recursion. This enables us to give a unified treatment of several interesting constructions including various universe constructions by Palmgren, Griffor, Rathjen, and Setzer and a constructive version of Aczel's Frege structures. Consistency of a restricted version of the extension is shown by constructing a realisability model in the style of Allen." @default.
• W2058174669 created "2016-06-24" @default.
• W2058174669 creator A5053761104 @default.
• W2058174669 date "2000-06-01" @default.
• W2058174669 modified "2023-10-17" @default.
• W2058174669 title "A general formulation of simultaneous inductive-recursive definitions in type theory" @default.
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• W2058174669 doi "https://doi.org/10.2307/2586554" @default.
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