Closedness properties in ex-identification

In this paper we investigate in which cases unions of identi$able classes are also necessarily identi$able. We consider identi$cation in the limit with bounds on mindchanges and anomalies. Though not closed under the set union, these identi$cation types still have features resembling closedness. For each of them we $nd n such that (1) if every union of n − 1 classes out of U1; : : : ; Un is identi$able, so is the union of all n classes; (2) there are classes U1; : : : ; Un−1 such that every union of n− 2 classes out of them is identi$able, while the union of n− 1 classes is not. We show that by $nding these n we can distinguish which requirements put on the identi$ability of unions of classes are satis$able and which are not. We also show how our problem is connected with team learning. c © 2001 Elsevier Science B.V. All rights reserved.