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Demuth’s path to randomness. (English) Zbl 1348.03002
This article surveys the work of Osvald Demuth, in particular, the notions of random real that he examined. The authors emphasize that Demuth was motivated by considerations of Russian-school constructive analysis, and he described these notions in terms of approximability, rather than randomness. This paper is based on an extended abstract written by A. Kučera and A. Nies [Lect. Notes Comput. Sci. 7160, 159–173 (2012; Zbl 1353.03047)]. However, the present version roughly triples the length of the earlier one, providing more background material and covering a wider span of Demuth’s output.

MSC:
03-03 History of mathematical logic and foundations
03D32 Algorithmic randomness and dimension
03D78 Computation over the reals, computable analysis
03F60 Constructive and recursive analysis
01A60 History of mathematics in the 20th century
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