INDUCTIVE INFERENCE UP TO IMMUNE SETS R 6si#g Freivalds aad Juris Viksaa Computing Center Latvian State University Riga, USSR Abstract We consider approximate in the limit of G6del numbers for total recursive functions. The set of possible errors is allowed to be infinite but "effectively small". The latter notion is precise in several ways. as "immune", "hyperimmune", "hyperhyperimrnune", "cohesive", etc. All the identification types considered tum out to the different. Introduction We are interested in inductive inference of G~el numbers of functions which can differ from the given function on an infinite but "small" set of values of the argument. The classical mathematics has developed a lot of distinct notions to express the "smallness". The most well-known of them is "small in terms of measure". Inference in the limit of GSdel numbers of functions which can differ from the given function on a set of bounded measure was studied thoroughly by K.Podnieks [8]. We consider the notion "small" in terms rather close to the "category". More precisely, we use notions of the theory of recursive functions to express the notion "effectively small".