Computable categoricity versus relative computable categoricity

Rodney G. Downey; Asher M. Kach; Steffen Lempp; Daniel D. Turetsky

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Computable analysis

Stanisław Mazur

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CONTENTS Foreword.......................................................................................... 3 I. Recursive and computable numbers...................................... 4 1. Recursive numbers................................................................... 5 2. Computable numbers............................................................... 17 II. Recursive and computable sequences................................. 22 III. Recursive and computable functionals....................................

Computable structures and operations on the space of continuous functions

Alexander G. Melnikov, Keng Meng Ng (2016)

Fundamenta Mathematicae

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We use ideas and machinery of effective algebra to investigate computable structures on the space C[0,1] of continuous functions on the unit interval. We show that (C[0,1],sup) has infinitely many computable structures non-equivalent up to a computable isometry. We also investigate if the usual operations on C[0,1] are necessarily computable in every computable structure on C[0,1]. Among other results, we show that there is a computable structure on C[0,1] which computes + and the scalar...