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Author: Richard L. Epstein
Publisher: American Mathematical Soc.
ISBN: 0821818627
Category : Constructive mathematics
Languages : en
Pages : 148
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Book Description
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.
Author: Richard L. Epstein
Publisher: American Mathematical Soc.
ISBN: 0821818627
Category : Constructive mathematics
Languages : en
Pages : 148
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Book Description
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.
Author: Manuel Lerman
Publisher: Cambridge University Press
ISBN: 131673935X
Category : Mathematics
Languages : en
Pages : 323
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Book Description
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.
Author: R. L. Epstein
Publisher: Springer
ISBN: 3540384804
Category : Mathematics
Languages : en
Pages : 255
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Book Description
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
Author: Richard L. Epstein
Publisher: American Mathematical Soc.
ISBN: 0821822411
Category : Recursion theory
Languages : en
Pages : 112
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Book Description
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.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 224
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Book Description
Author: Alexander S. Kechris
Publisher: Cambridge University Press
ISBN: 1316586286
Category : Mathematics
Languages : en
Pages : 552
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Book Description
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.
Author: E.R. Griffor
Publisher: Elsevier
ISBN: 0080533043
Category : Mathematics
Languages : en
Pages : 741
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Book Description
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.
Author: Arnold Beckmann
Publisher: Springer Science & Business Media
ISBN: 3540354662
Category : Computers
Languages : en
Pages : 623
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Book Description
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.
Author: F. R. Drake
Publisher: Cambridge University Press
ISBN: 052123543X
Category : Mathematics
Languages : en
Pages : 329
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Book Description
This book is a collection of advanced research/survey papers by eminent research workers in the Recursion theory.
Author: Robert I. Soare
Publisher: Springer
ISBN: 3642319335
Category : Computers
Languages : en
Pages : 289
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Book Description
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.
