Priority constructions (Q1923576)

Priority arguments are used in recursion theory to prove many theorems about the r.e. degrees. Usually one wants to construct a set (or sets). The basic idea is to write down the requirements you want your set to satisfy, order them in some way so that some requirements have priority over others, and then construct your set giving priority to the requirements of higher priority. In the course of the construction a requirement may become injured by the actions of a requirement of higher priority. In a finite-injury argument this can only happen to a particular requirement infinitely often. In an infinite-injury argument this may occur infinitely often. In this paper finite-injury and infinite-injury arguments are both put into (different) uniform frameworks. Virtually any finite-injury argument, and most infinite injury arguments (of type \(0''\)) can be put into this framework. Harder arguments, namely \(0'''\) arguments, can not.