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Two constructive embedding‐extension theorems with applications to continuity principles and to Banach‐Mazur computability

Andrej Bauer & Alex Simpson

Mathematical Logic Quarterly 50 (4‐5):351-369 (2004)

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A Banach–Mazur computable but not Markov computable function on the computable real numbers.Peter Hertling - 2005 - Annals of Pure and Applied Logic 132 (2-3):227-246.details We consider two classical computability notions for functions mapping all computable real numbers to computable real numbers. It is clear that any function that is computable in the sense of Markov, i.e., computable with respect to a standard Gödel numbering of the computable real numbers, is computable in the sense of Banach and Mazur, i.e., it maps any computable sequence of real numbers to a computable sequence of real numbers. We show that the converse is not true. This solves a (...) Download Export citation Bookmark 2 citations
Foundations of Constructive Analysis.Errett Bishop - 1967 - New York, NY, USA: Mcgraw-Hill.details This book, Foundations of Constructive Analysis, founded the field of constructive analysis because it proved most of the important theorems in real analysis by constructive methods. The author, Errett Albert Bishop, born July 10, 1928, was an American mathematician known for his work on analysis. In the later part of his life Bishop was seen as the leading mathematician in the area of Constructive mathematics. From 1965 until his death, he was professor at the University of California at San Diego. Download Export citation Bookmark 109 citations

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