Learnability and Positive Equivalence Relations

Prior work of Gavryushkin, Khoussainov, Jain and Stephan investigated what algebraic structures can be realised in worlds given by a positive (= recursively enumerable) equivalence relation which partitions the natural numbers into infinitely many classes. The present investigates infinite one-one numbered enumerable (r.e.) families such relations asks how choice impacts learnability properties these classes when studying limit from examples, also known as learning text. For all choices relations, for each following entries, there are r.e. satisfy it: (a) they behaviourally correctly learnable but not vacillatorily learnable; (b) explanatorily confidently (c) learnable. Furthermore, is enforces that (d) every family languages closed under this already cannot