The Emperor's New Recursiveness: The Epigraph of the Exponential Function in Two Models of Computability

Abstract

In his book \The Emperor’s New Mind" Roger Penrose implicitly denes 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.