Several authors (e.g. Jockusch, Appel, McLaughlin) use a notion of a regressive set, however none of the authors gives a complete definition, they refer to the paper J. C. E. Dekker, Infinite series of isols, Proc. Sympos. Pure Math. Vol. 5, pp. 77-96, Amer. Math. Soc., Providence, R. I., 1962. in the volume http://www.ams.org/books/pspum/005/ to which I, unfortunately, do not have the access.
So what is a definition of a regressive set?
Thanks to @Respawned Fluff for pointing out a more accessible resource.
Definition II.6.2 (Odifreddi vol. 1): If $\{a_o, a_1,a_2,...\}$ is an enumeration without repetitions of $A$, and $\phi$ is a partial recursive function such that $\phi(a_{n+1}) = a_n$ and $\phi(a_0) = a_0$, then $A$ is called regressive via $\phi$ and with respect to the given enumeration.