The paper presents a theorem which seems to capture essential combinatorial features common to all known finite-injury priority arguments in recursion theory and recursive model theory. In this sense the theorem can serve as a metatheorem for all such arguments, providing a general framework for them.

There are similar metatheorems of Ash and Knight (cf [1], [2], [3]) designed to do complicated a-nested priority arguments--they do not however apply to the classical Friedberg-Muchnik theorem. The statement of our metatheorem is as follows ...