Exploring further the properties of ITRM -recognizable reals started in [Ca], we provide a detailed analysis of recognizable reals and their distribution in Gödels constructible universe L. In particular, we show that new unrecognizables are generated at every index γ ≥ ω ω . We give a machine-independent characterization of recognizability by proving that a real r is recognizable iff it is Σ1-...
