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Computability and Logicby George S. Boolos; John P. Burgess; Richard C. Jeffrey
Cambridge University Press 2002; US$ 28.00Now in its fourth edition, this book has become a classic because it covers not simply the staple topics of intermediate logic courses but also a large number of other topics. John Burgess has enhanced the book by adding problems at the end of each chapter and by rewriting chapters. more...
Handbook of Computability Theoryby E.R. Griffor
Elsevier 1999; US$ 195.00The 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... more...
Computable Structures and the Hyperarithmetical Hierarchyby C.J. Ash; J. Knight
Elsevier 2000; US$ 133.00This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties). more...
Computability and Logicby George S. Boolos; John P. Burgess; Richard C. Jeffrey
Cambridge University Press 2007; US$ 26.00Computability and Logic is a classic because of its accessibility to students without a mathematical background. more...
New Computational Paradigmsby S.B. Cooper; Benedikt Lowe; Andrea Sorbi
Springer 2007; US$ 159.00Examines developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book covers topics in computability theory such as relative computability, theory of numberings, and domain theory. more...
Computability, Complexity, Logicby E. Börger
Elsevier 1989; US$ 189.00The theme of this book is formed by a pair of concepts: the concept of formal language as carrier of the precise expression of meaning, facts and problems, and the concept of algorithm or calculus, i.e. a formally operating procedure for the solution of precisely described questions and problems. The book is a unified introduction to the modern theory of these concepts, to the way in which they developed first in mathematical logic and computability theory and later in automata theory, and to the theory of formal languages and complexity theory. Apart from considering the fundamental themes and classical aspects of these areas, the subject matter has been selected to give priority throughout to the new aspects of traditional questions, results... more...
Proof theoryby Gaisi Takeuti
Elsevier Science & Technology 2000; US$ 250.00Provability, Computability and Reflection more...
Logic and Computationby Lawrence C. Paulson
Cambridge University Press 1987; US$ 49.00This book is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines the methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of program statements. Cambridge LCF is based on an earlier theorem-proving system, Edinburgh LCF, which introduced a design that gives the user flexibility to use and extend the system. A goal of this book is to explain the design, which has been adopted in several other systems. The book consists of two parts. Part I outlines the mathematical preliminaries, elementary logic and domain theory, and explains... more...
Computability Theoryby Herbert B. Enderton
Elsevier Science 2011; US$ 9.99Computability Theory more...
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