On the definitions of computable real continuous functions
Andrzej Grzegorczyk (1957)
Fundamenta Mathematicae
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Andrzej Grzegorczyk (1957)
Fundamenta Mathematicae
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Osvald Demuth (1988)
Commentationes Mathematicae Universitatis Carolinae
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Armin Hemmerling (2008)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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The first-value operator assigns to any sequence of partial functions of the same type a new such function. Its domain is the union of the domains of the sequence functions, and its value at any point is just the value of the first function in the sequence which is defined at that point. In this paper, the first-value operator is applied to establish hierarchies of classes of functions under various settings. For effective sequences of computable discrete functions, we obtain a hierarchy...
A. Janiczak (1954)
Colloquium Mathematicae
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Andrzej Mostowski (1955)
Fundamenta Mathematicae
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Rodney G. Downey, Asher M. Kach, Steffen Lempp, Daniel D. Turetsky (2013)
Fundamenta Mathematicae
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We study the notion of computable categoricity of computable structures, comparing it especially to the notion of relative computable categoricity and its relativizations. We show that every 1 decidable computably categorical structure is relatively Δ⁰₂ categorical. We study the complexity of various index sets associated with computable categoricity and relative computable categoricity. We also introduce and study a variation of relative computable categoricity, comparing it to both...
N. Routledge (1955)
Fundamenta Mathematicae
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Andrzej Mostowski (1957)
Fundamenta Mathematicae
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