Overgeneralization is a major issue in the identification of grammars for formal languages from positive data. Different formulations of generalization and specialization strategies have been proposed to address this problem, and recently there has been a flurry of activity investigating such strategies in the context of indexed families of recursive languages. The present paper studies the power of these strategies to learn recursively enumerable languages from positive data. In particular, the power of strong-monotonic, monotonic, and weak-monotonic (together with their dual notions modeling specialization) strategies are investigated for identification of r.e. languages. These investigations turn out to be different from the previous investigations on learning indexed families of recursive languages and at times require new proof techniques. A complete picture is provided for the relative power of each of the strategies considered. An interesting consequence is that the power ...