Index sets for classes of high rank structures
Wesley Calvert, Ekaterina Fokina, С. С. Гончаров, Julia F. Knight, Oleg V. Kudinov, Andrey S. Morozov, V. G. Puzarenko · Journal of Symbolic Logic · 2007
Abstract This paper calculates, in a precise way. the complexity of the index sets for three classes of computable structures: the class of structures of Scott rank , the class , of structures of Scott rank , and the class K of all structures of non-computable Scott rank. We show that I(K) is m-complete is m-complete relative to Kleene's and is m-complete relative to .