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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the eleventh publication in the Perspectives in Logic series, Manuel Lerman presents a systematic study of the interaction between local and global degree theory. He introduces the reader to the fascinating combinatorial methods of recursion theory while simultaneously showing how to use these methods to prove global theorems about degrees. The intended reader will have already taken a graduate-level course in recursion theory, but this book will also be accessible to those with some background in mathematical logic and a feeling for computability. It will prove a key reference to enable readers to easily locate facts about degrees and it will direct them to further results.

Unsolvability (Mathematical logic) --- Degrees of unsolvability --- Turing degrees of unsolvability --- Recursive functions

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Provability, Computability and Reflection

Logic, Symbolic and mathematical. --- Unsolvability (Mathematical logic) --- Degrees of unsolvability --- Turing degrees of unsolvability --- Recursive functions --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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Unsolvability (Mathematical logic) --- Combinatorial analysis --- Computable functions --- 510.6 --- #WWIS:ALTO --- Degrees of unsolvability --- Turing degrees of unsolvability --- Recursive functions --- Computability theory --- Functions, Computable --- Partial recursive functions --- Recursive functions, Partial --- Constructive mathematics --- Decidability (Mathematical logic) --- Combinatorics --- Algebra --- Mathematical analysis --- Mathematical logic --- Combinatorial analysis. --- Computable functions. --- Unsolvability (Mathematical logic). --- 510.6 Mathematical logic

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Computer science --- Mathematical logic --- Unsolvability (Mathematical logic) --- Fonctions récursives --- Recursive Functions --- Degrees of unsolvability --- Turing degrees of unsolvability --- Functions, Recursive --- Decidability (Mathematical logic) --- Computability theory --- Functions, Computable --- Partial recursive functions --- Recursive functions, Partial --- Fonctions récursives --- Computable functions --- Recursive functions --- 510.5 --- 510.5 Algorithms. Computable functions --- Algorithms. Computable functions --- Algorithms --- Arithmetic --- Logic, Symbolic and mathematical --- Number theory --- Recursion theory --- Constructive mathematics --- Foundations --- Fonctions calculables

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This book questions the relevance of computation to the physical universe. Our theories deliver computational descriptions, but the gaps and discontinuities in our grasp suggest a need for continued discourse between researchers from different disciplines, and this book is unique in its focus on the mathematical theory of incomputability and its relevance for the real world. The core of the book consists of thirteen chapters in five parts on extended models of computation; the search for natural examples of incomputable objects; mind, matter, and computation; the nature of information, complexity, and randomness; and the mathematics of emergence and morphogenesis. This book will be of interest to researchers in the areas of theoretical computer science, mathematical logic, and philosophy.

Computer science. --- Computers. --- Computer science --- Mathematical logic. --- Computer Science. --- Theory of Computation. --- Mathematics of Computing. --- Mathematical Logic and Foundations. --- Mathematics. --- Computable functions. --- Unsolvability (Mathematical logic) --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Degrees of unsolvability --- Turing degrees of unsolvability --- Computability theory --- Functions, Computable --- Partial recursive functions --- Recursive functions, Partial --- Constructive mathematics --- Decidability (Mathematical logic) --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Recursive functions --- Information theory. --- Informatics --- Science --- Communication theory --- Communication --- Cybernetics --- Computer science—Mathematics. --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Machine theory --- Calculators --- Cyberspace