The discrete parts of approximately decidable sets in Euclidean spaces

Abstract

It is shown that the classes of discrete parts, A ∩ N k , of approximately resp. weakly decidable subsets of Euclidean spaces, A ⊆ R k , coincide and are equal to the class of ω-r. e. sets which is well-known as the first transfinite level in Ershov's hierarchy exhausting ∆ 0 2 .