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  1. Diagonal Fixed Points in Algebraic Recursion Theory.Jordan Zashev - 2005 - Archive for Mathematical Logic 44 (8):973-994.
    The relation between least and diagonal fixed points is a well known and completely studied question for a large class of partially ordered models of the lambda calculus and combinatory logic. Here we consider this question in the context of algebraic recursion theory, whose close connection with combinatory logic recently become apparent. We find a comparatively simple and rather weak general condition which suffices to prove the equality of least fixed points with canonical (corresponding to those produced by the Curry (...)
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  • More Existence Theorems for Recursion Categories.Florian Lengyel - 2004 - Annals of Pure and Applied Logic 125 (1-3):1-41.
    We prove a generalization of Alex Heller's existence theorem for recursion categories; this generalization was suggested by work of Di Paola and Montagna on syntactic P-recursion categories arising from consistent extensions of Peano Arithmetic, and by the examples of recursion categories of coalgebras. Let B=BX be a uniformly generated isotypical B#-subcategory of an iteration category C, where X is an isotypical object of C. We give calculations for the existence of a weak Turing morphism in the Turing completion Tur of (...)
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  • Introduction to Turing Categories.J. Robin B. Cockett & Pieter Jw Hofstra - 2008 - Annals of Pure and Applied Logic 156 (2):183-209.
    We give an introduction to Turing categories, which are a convenient setting for the categorical study of abstract notions of computability. The concept of a Turing category first appeared in the work of Longo and Moggi; later, Di Paolo and Heller introduced the closely related recursion categories. One of the purposes of Turing categories is that they may be used to develop categorical formulations of recursion theory, but they also include other notions of computation, such as models of combinatory logic (...)
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