THE EMPEROR’S NEW RECURSIVENESS: THE EPIGRAPH OF THE EXPONENTIAL FUNCTION IN TWO MODELS OF COMPUTABILITY
Vasco Brattka · 2003
In his book “The Emperor’s New Mind ” Roger Penrose implicitly defines some criteria which should be met by a reasonable notion of recursiveness for subsets of Euclidean space. We discuss two such notions with regard to Penrose’s criteria: one originated from computable analysis, and the one introduced by Blum, Shub and Smale. 1