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Author : Rod Downey
Publisher :
ISBN 13 :
Total Pages : 49 pages
Book Rating : 4.:/5 (154 download)
Download or read book Computability, Definability and Algebraic Structures written by Rod Downey and published by . This book was released on 1999 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yuri L. Ershov
Publisher : Springer
ISBN 13 : 0306110393
Total Pages : 284 pages
Book Rating : 4.3/5 (61 download)
Download or read book Definability and Computability written by Yuri L. Ershov and published by Springer. This book was released on 1996-04-30 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Yurii L. Ershov posits the view that computability-in the broadest sense-can be regarded as the Sigma-definability in the suitable sets. He presents a new approach to providing the Gödel incompleteness theorem based on systematic use of the formulas with the restricted quantifiers. The volume also includes a novel exposition on the foundations of the theory of admissible sets with urelements, using the Gandy theorem throughout the theory's development. Other topics discussed are forcing, Sigma-definability, dynamic logic, and Sigma-predicates of finite types.
Author : Dimitŭr Genchev Skordev
Publisher : NATO Asi Series. Series C, Mat
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.:/5 (45 download)
Download or read book Computability in Combinatory Spaces written by Dimitŭr Genchev Skordev and published by NATO Asi Series. Series C, Mat. This book was released on 1992 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an account of the current state of the theory of combinatory spaces and discusses various applications. Here the term combinatory space can be regarded as a system for functional programming and bears no close connection with combinatory logic.
Author : Barry S. Cooper
Publisher : Springer Science & Business Media
ISBN 13 : 1461507553
Total Pages : 388 pages
Book Rating : 4.4/5 (615 download)
Download or read book Computability and Models written by Barry S. Cooper and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Science involves descriptions of the world we live in. It also depends on nature exhibiting what we can best describe as a high aLgorithmic content. The theme running through this collection of papers is that of the interaction between descriptions, in the form of formal theories, and the algorithmic content of what is described, namely of the modeLs of those theories. This appears most explicitly here in a number of valuable, and substantial, contributions to what has until recently been known as 'recursive model theory' - an area in which researchers from the former Soviet Union (in particular Novosibirsk) have been pre-eminent. There are also articles concerned with the computability of aspects of familiar mathematical structures, and - a return to the sort of basic underlying questions considered by Alan Turing in the early days of the subject - an article giving a new perspective on computability in the real world. And, of course, there are also articles concerned with the classical theory of computability, including the first widely available survey of work on quasi-reducibility. The contributors, all internationally recognised experts in their fields, have been associated with the three-year INTAS-RFBR Research Project "Com putability and Models" (Project No. 972-139), and most have participated in one or more of the various international workshops (in Novosibirsk, Heidelberg and Almaty) and otherresearch activities of the network.
Author : Antonio Montalbán
Publisher : Cambridge University Press
ISBN 13 : 1108534422
Total Pages : 214 pages
Book Rating : 4.1/5 (85 download)
Download or read book Computable Structure Theory written by Antonio Montalbán and published by Cambridge University Press. This book was released on 2021-06-24 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: In mathematics, we know there are some concepts - objects, constructions, structures, proofs - that are more complex and difficult to describe than others. Computable structure theory quantifies and studies the complexity of mathematical structures, structures such as graphs, groups, and orderings. Written by a contemporary expert in the subject, this is the first full monograph on computable structure theory in 20 years. Aimed at graduate students and researchers in mathematical logic, it brings new results of the author together with many older results that were previously scattered across the literature and presents them all in a coherent framework, making it easier for the reader to learn the main results and techniques in the area for application in their own research. This volume focuses on countable structures whose complexity can be measured within arithmetic; a forthcoming second volume will study structures beyond arithmetic.
Author : Peter Cholak
Publisher : American Mathematical Soc.
ISBN 13 : 0821819224
Total Pages : 338 pages
Book Rating : 4.8/5 (218 download)
Download or read book Computability Theory and Its Applications written by Peter Cholak and published by American Mathematical Soc.. This book was released on 2000 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles presents a snapshot of the status of computability theory at the end of the millennium and a list of fruitful directions for future research. The papers represent the works of experts in the field who were invited speakers at the AMS-IMS-SIAM 1999 Summer Conference on Computability Theory and Applications, which focused on open problems in computability theory and on some related areas in which the ideas, methods, and/or results of computability theory play a role. Some presentations are narrowly focused; others cover a wider area. Topics included from "pure" computability theory are the computably enumerable degrees (M. Lerman), the computably enumerable sets (P. Cholak, R. Soare), definability issues in the c.e. and Turing degrees (A. Nies, R. Shore) and other degree structures (M. Arslanov, S. Badaev and S. Goncharov, P. Odifreddi, A. Sorbi). The topics involving relations between computability and other areas of logic and mathematics are reverse mathematics and proof theory (D. Cenzer and C. Jockusch, C. Chong and Y. Yang, H. Friedman and S. Simpson), set theory (R. Dougherty and A. Kechris, M. Groszek, T. Slaman) and computable mathematics and model theory (K. Ambos-Spies and A. Kucera, R. Downey and J. Remmel, S. Goncharov and B. Khoussainov, J. Knight, M. Peretyat'kin, A. Shlapentokh).
Author : C.J. Ash
Publisher : Elsevier
ISBN 13 : 0080529526
Total Pages : 363 pages
Book Rating : 4.0/5 (85 download)
Download or read book Computable Structures and the Hyperarithmetical Hierarchy written by C.J. Ash and published by Elsevier. This book was released on 2000-06-16 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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).
Author : Stephan Foldes
Publisher : John Wiley & Sons
ISBN 13 : 1118031431
Total Pages : 362 pages
Book Rating : 4.1/5 (18 download)
Download or read book Fundamental Structures of Algebra and Discrete Mathematics written by Stephan Foldes and published by John Wiley & Sons. This book was released on 2011-02-14 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.
Author : S. Barry Cooper
Publisher : CRC Press
ISBN 13 : 1351991965
Total Pages : 428 pages
Book Rating : 4.3/5 (519 download)
Download or read book Computability Theory written by S. Barry Cooper and published by CRC Press. This book was released on 2017-09-06 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.
Author : Peter Cholak
Publisher : Cambridge University Press
ISBN 13 : 1108659934
Total Pages : 195 pages
Book Rating : 4.1/5 (86 download)
Download or read book The Notre Dame Lectures written by Peter Cholak and published by Cambridge University Press. This book was released on 2017-03-30 with total page 195 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 the fall of 2000, the logic community at the University of Notre Dame, Indiana hosted Greg Hjorth, Rodney G. Downey, Zoé Chatzidakis and Paola D'Aquino as visiting lecturers. Each of them presented a month-long series of expository lectures at the graduate level. This volume, the eighteenth publication in the Lecture Notes in Logic series, contains refined and expanded versions of those lectures. The four articles are entitled 'Countable models and the theory of Borel equivalence relations', 'Model theory of difference fields', 'Some computability-theoretic aspects of reals and randomness' and 'Weak fragments of Peano arithmetic'.
Author : I︠U︡riĭ Leonidovich Ershov
Publisher : Springer Science & Business Media
ISBN 13 : 9780306110399
Total Pages : 288 pages
Book Rating : 4.1/5 (13 download)
Download or read book Definability and Computability written by I︠U︡riĭ Leonidovich Ershov and published by Springer Science & Business Media. This book was released on 1996-04-30 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Yurii L. Ershov posits the view that computability-in the broadest sense-can be regarded as the Sigma-definability in the suitable sets. He presents a new approach to providing the Gödel incompleteness theorem based on systematic use of the formulas with the restricted quantifiers. The volume also includes a novel exposition on the foundations of the theory of admissible sets with urelements, using the Gandy theorem throughout the theory's development. Other topics discussed are forcing, Sigma-definability, dynamic logic, and Sigma-predicates of finite types.
Author : S Barry Cooper
Publisher : World Scientific
ISBN 13 : 1908978767
Total Pages : 419 pages
Book Rating : 4.9/5 (89 download)
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
Author : Mariko Yasugi
Publisher : World Scientific
ISBN 13 : 9814486779
Total Pages : 481 pages
Book Rating : 4.8/5 (144 download)
Download or read book Proceedings Of The 7th And 8th Asian Logic Conferences written by Mariko Yasugi and published by World Scientific. This book was released on 2003-11-11 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 7th and the 8th Asian Logic Conferences belong to the series of logic conferences inaugurated in Singapore in 1981. This meeting is held once every three years and rotates among countries in the Asia-Pacific region, with interests in the broad area of logic, including theoretical computer science. It is now considered a major conference in this field and is regularly sponsored by the Association for Symbolic Logic.This book contains papers — many of them surveys by leading experts — of both the 7th meeting (in Hsi-Tou, Taiwan) and the 8th (in Chongqing, China). The volume planned for the 7th meeting was interrupted by the earthquake in Taiwan and the decision was made to combine the two proceedings. The 8th conference is also the ICM2002 Satellite Conference on Mathematical Logic.
Author : Noam Greenberg
Publisher : Cambridge University Press
ISBN 13 : 110751200X
Total Pages : 205 pages
Book Rating : 4.1/5 (75 download)
Download or read book Effective Mathematics of the Uncountable written by Noam Greenberg and published by Cambridge University Press. This book was released on 2013-10-31 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods – some old, some new – that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students and a source of interesting new approaches for researchers in computability theory and related areas.
Author : Cyrus F. Nourani
Publisher : CRC Press
ISBN 13 : 1771882484
Total Pages : 304 pages
Book Rating : 4.7/5 (718 download)
Download or read book Algebraic Computability and Enumeration Models written by Cyrus F. Nourani and published by CRC Press. This book was released on 2016-02-24 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples
Author : Douglas Cenzer
Publisher : World Scientific Publishing Company
ISBN 13 : 9789813228221
Total Pages : 200 pages
Book Rating : 4.2/5 (282 download)
Download or read book Computability, Forcing and Descriptive Set Theory written by Douglas Cenzer and published by World Scientific Publishing Company. This book was released on 2019-12-31 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra, analysis and topology. These include effective versions of Borel equivalence, Borel reducibility and Borel determinacy. It also covers algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Many of these topics are being discussed in the NSF-supported annual Southeastern Logic Symposium. Contents: Limits of the Kucerea-Gacs Coding Method (George Barmpalias and Andrew Lewis-Pye);Infinitary partition properties of sums of selective ultrafilters (Andreas Blass);Semiselective Coideals and Ramsey Sets (Carlos DiPrisco and Leonardo Pacheco);Survey on Topological Ramsey Spaces Dense in Forcings (Natasha Dobrinen);Higher Computability in the Reverse Mathematics of Borel Determinacy (Sherwood Hachtman);Computability and Definability (Valentina Harizanov);A Ramsey Space of Infinite Polyhedra and the Random Polyhedron (Jose G Mijares Palacios and Gabriel Padilla);Computable Reducibility for Cantor Space (Russell G Miller);Information vs Dimension - An Algorithmic Perspective (Jan Reimann); Readership: Graduate students and researchers interested in the interface between set theory and computability.
Author : S. Abramsky
Publisher : OUP Oxford
ISBN 13 : 0191546275
Total Pages : 556 pages
Book Rating : 4.1/5 (915 download)
Download or read book Handbook of Logic in Computer Science: Volume 5. Algebraic and Logical Structures written by S. Abramsky and published by OUP Oxford. This book was released on 2001-01-25 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook volume covers fundamental topics of semantics in logic and computation. The chapters (some monographic in length), were written following years of co-ordination and follow a thematic point of view. The volume brings the reader up to front line research, and is indispensable to any serious worker in the areas.
