ABSTRACT The aim of this study is to give natural examples of ‐complete and ‐complete sets. In the first part, we consider ideals on . We use a unified approach introduced in 4 to create reductions of the collection of ill‐founded trees to the ideals, proving ‐completeness of the ideals. In the second part, we show the connection between this topic, families of trees and coding of ‐ideals of Polish spaces. In particular, we use the unified approach to prove that sets of codes for closed Ramsey‐null sets, for closed ‐compact sets and for closed not strongly dominating sets are ‐complete.
Mazurkiewicz et al. (Sun,) studied this question.