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RESEARCH PRODUCT

Closedness properties in team learning of recursive functions

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This paper investigates closedness properties in relation with team learning of total recursive functions. One of the first problems solved for any new identification types is the following: “Does the identifiability of classes U1 and U2 imply the identifiability of U1∪U2?” In this paper we are interested in a more general question: “Does the identifiability of every union of n−1 classes out of U1,...,Un imply the identifiability of U1∪...∪Un?” If the answer is positive, we call such identification type n-closed. We show that n-closedness can be equivalently formulated in terms of team learning. After that we find for which n team identification in the limit and team finite identification types are n-closed. In the case of team finite identification only teams in which at least half of the strategies must be successful are considered. It turns out that all these identification types, though not closed in the usual sense, are n-closed for some n>2.