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Minimal Degrees Of Unsolvability And The Full Approximation Construction
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Book Synopsis Minimal Degrees of Unsolvability and the Full Approximation Construction by : Richard L. Epstein
Download or read book Minimal Degrees of Unsolvability and the Full Approximation Construction written by Richard L. Epstein and published by American Mathematical Soc.. This book was released on 1975 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the purposes of this monograph, "by a degree" is meant a degree of recursive unsolvability. A degree [script bold]m is said to be minimal if 0 is the unique degree less than [script bold]m. Each of the six chapters of this self-contained monograph is devoted to the proof of an existence theorem for minimal degrees.
Book Synopsis Degrees of Unsolvability by : Manuel Lerman
Download or read book Degrees of Unsolvability written by Manuel Lerman and published by Cambridge University Press. This book was released on 2017-04-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Degrees of Unsolvability by : R. L. Epstein
Download or read book Degrees of Unsolvability written by R. L. Epstein and published by Springer. This book was released on 2006-11-15 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex interactions of economic, technological, political, and cultural factors have fed the rise of criminal networks worldwide. At the same time, global illegal activities depend on a world of social realities to function. Organized Crime moves beyond traditional concepts of "evil forces" corrupting their host societies, instead analyzing local, national, and international manifestations of organized crime in the situational contexts that aid in its development. The contributors provide up-to-date understanding of various aspects of organized crime, in both classic areas of research (drugs, sex trafficking, labor racketeering) and emerging areas of interest (diamond smuggling, money laundering, eco-crime), in locales as varied as Italy, Quebec, the Sinai, Bulgaria, and the world's tropical rain forests. Topics are explored from a variety of perspectives, including sociology, criminology, political science, and anthropology, giving this book empirical breadth and depth rarely seen in the literature. A sampling of the topics: Symbolic and economic meanings of crime to cultures. The symbiotic relationships between legitimate and criminal activities. Ethical dilemmas of legitimate businesses with criminal clients. Marketing, problem-solving, recruitment: organizational models of criminal enterprises. Innovative law enforcement/administrative strategies for containing and preventing crime in the U.S. and across Europe. Scholars and researchers of organized crime as well as advanced students of criminology will welcome Organized Crime for coverage that is wide-ranging, comparative, and specific enough to match their interests
Book Synopsis Initial Segments of Degrees Below $\underline {0}^\prime $ by : Richard L. Epstein
Download or read book Initial Segments of Degrees Below $\underline {0}^\prime $ written by Richard L. Epstein and published by American Mathematical Soc.. This book was released on 1981 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove two main results: (1) [lowercase Greek]Omega + 1 is an initial segment of the degrees ([less-than or equal to]≤ a̲ for any r.e. a̲ [not equal to] 0̲ , and (2) given any 0̲ [less than] a̲ [less than] h̲ where a̲ and h̲ are r.e. and h̲ is high, there is a minimal degree m̲ [less than] h̲ such that m̲ [set-theoretic union] a̲ = h̲.
Book Synopsis Canadian Journal of Mathematics by :
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1977-10 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ordinal Definability and Recursion Theory: Volume 3 by : Alexander S. Kechris
Download or read book Ordinal Definability and Recursion Theory: Volume 3 written by Alexander S. Kechris and published by Cambridge University Press. This book was released on 2016-01-11 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.
Book Synopsis Handbook of Computability Theory by : E.R. Griffor
Download or read book Handbook of Computability Theory written by E.R. Griffor and published by Elsevier. This book was released on 1999-10-01 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.
Book Synopsis Logical Approaches to Computational Barriers by : Arnold Beckmann
Download or read book Logical Approaches to Computational Barriers written by Arnold Beckmann and published by Springer Science & Business Media. This book was released on 2006-06-26 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, June/July 2006. The book presents 31 revised full papers together with 30 invited papers, including papers corresponding to 8 plenary talks and 6 special sessions on proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and Gödel centenary: Gödel's legacy for computability.
Book Synopsis Recursion Theory, Its Generalisations and Applications by : F. R. Drake
Download or read book Recursion Theory, Its Generalisations and Applications written by F. R. Drake and published by Cambridge University Press. This book was released on 1980-11-13 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of advanced research/survey papers by eminent research workers in the Recursion theory.
Book Synopsis Turing Computability by : Robert I. Soare
Download or read book Turing Computability written by Robert I. Soare and published by Springer. This book was released on 2016-06-20 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Turing's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic. The author presents the subject as an art to be practiced, and an art in the aesthetic sense of inherent beauty which all mathematicians recognize in their subject. Part I gives a thorough development of the foundations of computability, from the definition of Turing machines up to finite injury priority arguments. Key topics include relative computability, and computably enumerable sets, those which can be effectively listed but not necessarily effectively decided, such as the theorems of Peano arithmetic. Part II includes the study of computably open and closed sets of reals and basis and nonbasis theorems for effectively closed sets. Part III covers minimal Turing degrees. Part IV is an introduction to games and their use in proving theorems. Finally, Part V offers a short history of computability theory. The author has honed the content over decades according to feedback from students, lecturers, and researchers around the world. Most chapters include exercises, and the material is carefully structured according to importance and difficulty. The book is suitable for advanced undergraduate and graduate students in computer science and mathematics and researchers engaged with computability and mathematical logic.
Download or read book Logic Year 1979-80 written by M. Lerman and published by Springer. This book was released on 2006-11-15 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computability In Context: Computation And Logic In The Real World by : S Barry Cooper
Download or read book Computability In Context: Computation And Logic In The Real World written by S Barry Cooper and published by World Scientific. This book was released on 2011-02-25 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability has played a crucial role in mathematics and computer science, leading to the discovery, understanding and classification of decidable/undecidable problems, paving the way for the modern computer era, and affecting deeply our view of the world. Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions about the so-called Turing barrier.This volume addresses various aspects of the ways computability and theoretical computer science enable scientists and philosophers to deal with mathematical and real-world issues, covering problems related to logic, mathematics, physical processes, real computation and learning theory. At the same time it will focus on different ways in which computability emerges from the real world, and how this affects our way of thinking about everyday computational issues./a
Book Synopsis Dictionary of World Philosophy by : A. Pablo Iannone
Download or read book Dictionary of World Philosophy written by A. Pablo Iannone and published by Routledge. This book was released on 2013-04-15 with total page 894 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Dictionary of World Philosophy covers the diverse and challenging terminology, concepts, schools and traditions of the vast field of world philosophy. Providing an extremely comprehensive resource and an essential point of reference in a complex and expanding field of study the Dictionary covers all major subfields of the discipline. Key features: * Cross-references are used to highlight interconnections and the cross-cultural diffusion and adaptation of terms which has taken place over time * The user is led from specific terms to master entries which provide valuable historical and cultural context * Each master entry is followed by at least two suggestions for further reading on the subject, creating a substantial bibliography of world philosophy * References extend beyond philosophy to related areas such as cognitive science, computer science, language and physics Subdisciplines covered include:* aesthetics * ethics * sociopolitical philosophy * the philosophy of law * epistemology * logic * the philosophy of science * the philosophy of mind * the philosophy of culture and history * metaphysics * the philosophy of religion Entries are drawn from West Africa, Arabic, Chinese, Indian, Japanese, Jewish, Korean, Latin American, Maori and Native American philosophy including the important and so far largely neglected instance of Pre-Hispanic thought: Nahua philosophy.
Book Synopsis Computability, Enumerability, Unsolvability by : S. B. Cooper
Download or read book Computability, Enumerability, Unsolvability written by S. B. Cooper and published by Cambridge University Press. This book was released on 1996-01-11 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book, by leaders in the field, provide a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory. The topics range over computable functions, enumerable sets, degree structures, complexity, subrecursiveness, domains and inductive inference. A number of the articles contain introductory and background material which it is hoped will make this volume an invaluable resource.
Book Synopsis Classical Recursion Theory by : P. Odifreddi
Download or read book Classical Recursion Theory written by P. Odifreddi and published by Elsevier. This book was released on 1992-02-04 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.
Book Synopsis Notices of the American Mathematical Society by : American Mathematical Society
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1981 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 1999 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt:
