An usual classification of undecidable problems in computability theory is the one given by the arithmetical hierarchy introduced by Kleene. Very recently. L. Blum, M. Shub and S. Smale devised a model of computation able to work with real numbers and showed the main properties of a computability theory for that model. In this paper we introduce the arithmetical hierarchy for it. A syntactical characterization is given, together with some complete problems. Also, it is shown that if nondeterministic machines are considered instead of deterministic ones, a different set of classes is obtained (unlike the classical case) and all these classes are related with the classification of sets of reals done in descriptive set theory. © 1992 Oxford University Press.
CITATION STYLE
Cucker, F. (1992). The arithmetical hierarchy over the reals. Journal of Logic and Computation, 2(3), 375–395. https://doi.org/10.1093/logcom/2.3.375
Mendeley helps you to discover research relevant for your work.