Theory of Formal Systems
Theory of Formal Systems

Author: Raymond M. Smullyan

Publisher: Princeton University Press

Published: 1961

Total Pages: 160

ISBN-13: 9780691080475

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This book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems.

Classical Recursion Theory
Classical Recursion Theory

Author: P. Odifreddi

Publisher: Elsevier

Published: 1992-02-04

Total Pages: 667

ISBN-13: 9780080886596

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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.

Computability Theory
Computability Theory

Author: Neil D. Jones

Publisher: Academic Press

Published: 2014-06-20

Total Pages: 169

ISBN-13: 1483218481

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Computability Theory: An Introduction provides information pertinent to the major concepts, constructions, and theorems of the elementary theory of computability of recursive functions. This book provides mathematical evidence for the validity of the Church–Turing thesis. Organized into six chapters, this book begins with an overview of the concept of effective process so that a clear understanding of the effective computability of partial and total functions is obtained. This text then introduces a formal development of the equivalence of Turing machine computability, enumerability, and decidability with other formulations. Other chapters consider the formulas of the predicate calculus, systems of recursion equations, and Post's production systems. This book discusses as well the fundamental properties of the partial recursive functions and the recursively enumerable sets. The final chapter deals with different formulations of the basic ideas of computability that are equivalent to Turing-computability. This book is a valuable resource for undergraduate or graduate students.

Proof Theory
Proof Theory

Author: Wolfram Pohlers

Publisher: Springer Science & Business Media

Published: 2008-10-01

Total Pages: 380

ISBN-13: 354069319X

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The kernel of this book consists of a series of lectures on in?nitary proof theory which I gave during my time at the Westfalische ̈ Wilhelms–Universitat ̈ in Munster ̈ . It was planned as a successor of Springer Lecture Notes in Mathematics 1407. H- ever, when preparing it, I decided to also include material which has not been treated in SLN 1407. Since the appearance of SLN 1407 many innovations in the area of - dinal analysis have taken place. Just to mention those of them which are addressed in this book: Buchholz simpli?ed local predicativity by the invention of operator controlled derivations (cf. Chapter 9, Chapter 11); Weiermann detected applications of methods of impredicative proof theory to the characterization of the provable recursive functions of predicative theories (cf. Chapter 10); Beckmann improved Gentzen’s boundedness theorem (which appears as Stage Theorem (Theorem 6. 6. 1) in this book) to Theorem 6. 6. 9, a theorem which is very satisfying in itself - though its real importance lies in the ordinal analysis of systems, weaker than those treated here. Besides these innovations I also decided to include the analysis of the theory (? –REF) as an example of a subtheory of set theory whose ordinal analysis only 2 0 requires a ?rst step into impredicativity. The ordinal analysis of(? –FXP) of non- 0 1 0 monotone? –de?nable inductive de?nitions in Chapter 13 is an application of the 1 analysis of(? –REF).

Advances in Software Science and Technology
Advances in Software Science and Technology

Author: Yoshio Ohno

Publisher: Elsevier

Published: 2014-12-01

Total Pages: 232

ISBN-13: 1483215709

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Advances in Software Science and Technology, Volume 2 provides information pertinent to the advancement of the science and technology of computer software. This book discusses the various applications for computer systems. Organized into four parts encompassing 12 chapters, this volume begins with an overview of categorical frameworks that are widely used to represent data types in computer science. This text then provides an algorithm for generating vertices of a smoothed polygonal line from the vertices of a digital curve or polygonal curve whose position contains a certain amount of error. Other chapters consider a system that automatically synthesizes a program from a specification written in natural language. The final chapter deals with the rules for submission of English papers that will be published, which includes papers that are reports of academic research by members of the Society. This book is a valuable resource for scientists and research workers.

The Theory of Models
The Theory of Models

Author: J.W. Addison

Publisher: Elsevier

Published: 2014-05-27

Total Pages: 513

ISBN-13: 1483275345

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Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis's systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders on Boolean notions extended to higher dimensions, elementary theories with models without automorphisms, and applications of the notions of forcing and generic sets. The manuscript takes a look at a hypothesis concerning the extension of finite relations and its verification for certain special cases, theories of functors and models, model-theoretic methods in the study of elementary logic, and extensions of relational structures. The text also reviews relatively categorical and normal theories, algebraic theories, categories, and functors, denumerable models of theories with extra predicates, and non-standard models for fragments of number theory. The selection is highly recommended for mathematicians and researchers interested in the theory of models.