Name
Abstract | ||
|---|---|---|
Osvald Demuth (1936---1988) studied constructive analysis in the Russian style. For this he introduced notions of effective null sets which, when phrased in classical language, yield major algorithmic randomness notions. He proved several results connecting constructive analysis and randomness that were rediscovered only much later. We give an overview in mostly chronological order. We sketch a proof that Demuth's notion of Denjoy sets (or reals) coincides with computable randomness. We show that he worked with a test notion that is equivalent to Schnorr tests relative to the halting problem. We also discuss the invention of Demuth randomness, and Demuth's and Kučera's work on semigenericity. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/978-3-642-27654-5_12 | Computation, Physics and Beyond |
Keywords | Field | DocType |
demuth randomness,test notion,classical language,russian style,major algorithmic randomness notion,constructive analysis,computable randomness,effective null set,chronological order,osvald demuth | Discrete mathematics,Algebra,Classical language,Algorithmic randomness,Turing degree,Halting problem,Mathematics,Computable function,Sketch,Randomness,Constructive analysis | Conference |
Citations | PageRank | References |
1 | 0.61 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Antonín Kučera | 1 | 262 | 18.04 |
| André Nies | 2 | 325 | 50.82 |
| Christopher P. Porter | 3 | 8 | 5.93 |