C.E. Degrees and the Priority Method

Abstract

Among the Turing degrees, the so-called computably enumerable (c.e.) degrees are all-important. This is because they stem from c.e. sets, the sets that often spring up in practice. In this chapter we will present the basic facts of c.e. degrees. We will then describe Post’s Problem, a problem about c.e. degrees that was posed by Emil Post in 1944. After a series of attempts by Post and others, the problem was finally solved in 1956 by Muchnik and Friedberg. They simultaneously and independently devised a method, called the Priority Method, and applied it to solve the problem. We will describe Post’s Problem and the Priority Method.

If something has priority over other things, it is regarded as being more important than them and is dealt with first. An injury is damage done to somebody’s body.