Sharif Digital Repository

One of the the most fundamental questions in computability (recursion) theory is the exact structure of D and in particular that of R. Over the years, various efforts have eventuated in Degree ?eory, an interesting subfield of computability theory, which is concerned with various properties of these algebraic structures which have turned out to be extremely complex. Beyond any doubt, the most useful tool for proving theorems related toRis the Priority Method which is first introduced to solve the Post’s problem. Over the years, increasingly more sophisticated versions of the method have been used to prove complex statements about R. Roughly one may classify the priority arguments into three...