Agreement reducibility

Abstract

We introduce agreement reducibility and highlight its major features. Given subsets A and B of N, we write A ≤ agree B if there is a total computable function f : N → N satisfying for all e, e , W e ∩ A = W e ∩ A if and only if W f (e) ∩ B = W f (e) ∩ B. We shall discuss the central role N plays in this reducibility and its connection to strong-hyper-hyper-immunity. We shall also compare agreement reducibility to other well-known reducibilities, in particular s 1-and s-reducibility. We came upon this reducibility while studying the computable reducibility of a class of equivalence relations on N based on set-agreement. We end by describing the origin of agreement reducibility and presenting some results in that context.