The algebraic systems of combinatory spaces [3] and operative spaces [1] have been designed to provide appropriate settings for the development of abstract recursion theory. As shown in [1, Chapter 27], these systems are closely related; namely, every combinatory space has a companion operative space with a storing operation St such that Skordev recursiveness in the former equals st-recursiveness in the latter. The problem of characterization of those operative spaces which have companion combinatory spaces was solved in [2] by introducing a class of operative spaces called Skordev spaces and showing that these give an alternative axiomatics of Skordev's combinatory spaces.

In this paper we study operative spaces with two special constants S1 and S2 which, in computer science terms, axiomatize the availability of stacking facility. We establish that any such space has a Skordev subspace and, moreover, all Skordev spaces can be obtained in this way. The construction ensures that st-recursiveness in the Skordev space concerned is equivalent to recursiveness in S1 and S2 in the wider operative space. Therefore, it quite unexpectedly turns out that Skordev recursiveness can be expressed via relative recursiveness in operative spaces in a straightforward manner, without employing higher spaces as done in [1].