Computable Structure Theory
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Computable Structure Theory
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Author : Antonio Montalbán
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-24
Computable Structure Theory written by Antonio Montalbán and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-24 with Mathematics categories.
Presents main results and techniques in computable structure theory together in a coherent framework for the first time in 20 years.
Computable Structures And The Hyperarithmetical Hierarchy
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Author : C.J. Ash
language : en
Publisher: Elsevier
Release Date : 2000-06-16
Computable Structures And The Hyperarithmetical Hierarchy written by C.J. Ash and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-16 with Mathematics categories.
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).
Structure And Randomness In Computability And Set Theory
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Author : Douglas Cenzer
language : en
Publisher: World Scientific
Release Date : 2020-10-02
Structure And Randomness In Computability And Set Theory written by Douglas Cenzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-02 with Mathematics categories.
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.
Reflexive Structures
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Author : Luis E. Sanchis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Reflexive Structures written by Luis E. Sanchis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Reflexive Structures: An Introduction to Computability Theory is concerned with the foundations of the theory of recursive functions. The approach taken presents the fundamental structures in a fairly general setting, but avoiding the introduction of abstract axiomatic domains. Natural numbers and numerical functions are considered exclusively, which results in a concrete theory conceptually organized around Church's thesis. The book develops the important structures in recursive function theory: closure properties, reflexivity, enumeration, and hyperenumeration. Of particular interest is the treatment of recursion, which is considered from two different points of view: via the minimal fixed point theory of continuous transformations, and via the well known stack algorithm. Reflexive Structures is intended as an introduction to the general theory of computability. It can be used as a text or reference in senior undergraduate and first year graduate level classes in computer science or mathematics.
Computability Theory
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Author : S. Barry Cooper
language : en
Publisher: CRC Press
Release Date : 2017-09-06
Computability Theory written by S. Barry Cooper and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Mathematics categories.
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.
Computability And Complexity
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Author : Adam Day
language : en
Publisher: Springer
Release Date : 2016-11-30
Computability And Complexity written by Adam Day and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-30 with Computers categories.
This Festschrift is published in honor of Rodney G. Downey, eminent logician and computer scientist, surfer and Scottish country dancer, on the occasion of his 60th birthday. The Festschrift contains papers and laudations that showcase the broad and important scientific, leadership and mentoring contributions made by Rod during his distinguished career. The volume contains 42 papers presenting original unpublished research, or expository and survey results in Turing degrees, computably enumerable sets, computable algebra, computable model theory, algorithmic randomness, reverse mathematics, and parameterized complexity, all areas in which Rod Downey has had significant interests and influence. The volume contains several surveys that make the various areas accessible to non-specialists while also including some proofs that illustrate the flavor of the fields.
A First Course In Logic
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Author : Shawn Hedman
language : en
Publisher: OUP Oxford
Release Date : 2004-07-08
A First Course In Logic written by Shawn Hedman and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-08 with Mathematics categories.
The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course.
Handbook Of Computability Theory
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Author : E.R. Griffor
language : en
Publisher: Elsevier
Release Date : 1999-10-01
Handbook Of Computability Theory written by E.R. Griffor and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-01 with Mathematics categories.
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.
A Hierarchy Of Turing Degrees
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Author : Rod Downey
language : en
Publisher: Princeton University Press
Release Date : 2020-06-16
A Hierarchy Of Turing Degrees written by Rod Downey and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-16 with Mathematics categories.
Computability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field has developed growing connections in diverse areas of mathematics, with applications in topology, group theory, and other subfields. In A Hierarchy of Turing Degrees, Rod Downey and Noam Greenberg introduce a new hierarchy that allows them to classify the combinatorics of constructions from many areas of computability theory, including algorithmic randomness, Turing degrees, effectively closed sets, and effective structure theory. This unifying hierarchy gives rise to new natural definability results for Turing degree classes, demonstrating how dynamic constructions become reflected in definability. Downey and Greenberg present numerous construction techniques involving high-level nonuniform arguments, and their self-contained work is appropriate for graduate students and researchers. Blending traditional and modern research results in computability theory, A Hierarchy of Turing Degrees establishes novel directions in the field.
New Computational Paradigms
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Author : S.B. Cooper
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-28
New Computational Paradigms written by S.B. Cooper and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-28 with Computers categories.
This superb exposition of a complex subject examines new 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 is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.