Degrees of Unsolvability: Local and Global Theory (Perspectives in mathematical logic)

US: Springer-Verlag, 1983. Ex-Lib. Hardcover. Very Good-/None. Perspectives in Mathematical Logic Ser. Yellow cloth boards, toned and lightly soiled from fingerprints. Interior is clean, and text is unmarked. Pastedowns are scarred where bookplates removed. Binding is sound. 8vo. BOOK INFO: See photos for Table of Contents. 'Degree theory, as it is studied today, traces its development back to the fundamental papers of...Kleene and Post [which] introduced algebraic structures which arise naturally from the classification of sets of natural numbers in terms of the amount of additional oracular information needed to compute these sets....The idea of comparing sets in terms of the amount of information needed to compute them has been extended to notions of computability or constructibility which are relevant to other areas of Mathematical Logic such as Set Theory, Descriptive Set Theory, and Computational Complexity as well as Recursion Theory. However, the most widely studied notion of degree is still that of degree of unsolvability or Turing Degree. The interest in this area lies as much in the fascinating combinatorial proofs which seem to be needed to obtain the results as in the attempt to unravel the mysteries of the structure. An attmept is made, in this book, to present a study of the degrees which emphasizes the methods of proof as well as the results. We also try to give the reader a feeling for the usefulness of local structure theory in determining global properties of the degrees, properties which deal with questions about homogeneity, automorphisms, decidability and definability.' (~from the Introduction \nIncludes indexes. Unsolvability (Mathematical logic)