Closedness Properties In Ex-Identification Of Recursive Functions

In this paper we investigate in which cases unions of identifiable classes of recursive functions are also necessarily identifiable. We consider identification in the limit with bounds on mindchanges and anomalies. Though not closed under the set union, these identification types still have features resembling closedness. For each of them we find such n that1) if every union of n - 1 classes out of U-1, ..., U-n is identifiable, so is the union of all n classes;2) there are such classes U-1, ..., Un-1 that every union of n - 2 classes out of them is identifiable, while the union of n - 1 classes is not.We show that by finding these n, we can distinguish which requirements put on the identifiability of unions of classes are satisfiable and which are not. We also show how our problem is connected with team learning.