Angluin's Theorem for Indexed Families of R.E. Sets and Applications Dick de Jongh, Makoto Kanazawa Abstract: We extend Angluin's (1980) theorem to characterize identifiability of indexed families of r.e. languages, as opposed to indexed families of recursive languages. We also prove some variants characterizing conservativity and two other similar restrictions, paralleling Zeugmann, Lange, and Kapur's (1992, 1995) results for indexed families of recursive languages.