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Computable Structures And The Hyperarithmetical Hierarchy

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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).

Computable Structures And The Hyperarithmetical Hierarchy

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Author : C.J. Ash
language : en
Publisher: Elsevier Science
Release Date : 2000-06-16

Computable Structures And The Hyperarithmetical Hierarchy written by C.J. Ash and has been published by Elsevier Science this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-16 with Mathematics categories.

Handbook Of The History And Philosophy Of Mathematical Practice

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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date : 2024-04-26

Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.

The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques

The Nature Of Computation Logic Algorithms Applications

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Author : Paola Bonizzoni
language : en
Publisher: Springer
Release Date : 2013-06-03

The Nature Of Computation Logic Algorithms Applications written by Paola Bonizzoni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-03 with Computers categories.

This book constitutes the refereed proceedings of the 9th Conference on Computability in Europe, CiE 2013, held in Milan, Italy, in July 2013. The 48 revised papers presented together with 1 invited lecture and 2 tutorials were carefully reviewed and selected with an acceptance rate of under 31,7%. Both the conference series and the association promote the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences such as physics and biology, and also including the promotion of related non-scientific fields such as philosophy and history of computing.

Well Quasi Orders In Computation Logic Language And Reasoning

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Author : Peter M. Schuster
language : en
Publisher: Springer Nature
Release Date : 2020-01-01

Well Quasi Orders In Computation Logic Language And Reasoning written by Peter M. Schuster and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-01 with Philosophy categories.

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.

Effective Mathematics Of The Uncountable

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Author : Noam Greenberg
language : en
Publisher: Cambridge University Press
Release Date : 2013-10-31

Effective Mathematics Of The Uncountable written by Noam Greenberg 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 2013-10-31 with Mathematics categories.

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.

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.

Twenty Years Of Theoretical And Practical Synergies

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Author : Ludovic Levy Patey
language : en
Publisher: Springer Nature
Release Date : 2024-07-01

Twenty Years Of Theoretical And Practical Synergies written by Ludovic Levy Patey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-01 with Computers categories.

This book constitutes the refereed proceedings of the 20th Conference on Computabilitty in Europe, CiE 2024, held in Amsterdam, The Netherlands, during July 8–12, 2024 The 26 full papers and 2 short papers included in this book were carefully reviewed and selected from 43 submissions. This CIE 2024 focus on development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences.

Theory And Applications Of Models Of Computation

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Author : T.V. Gopal
language : en
Publisher: Springer
Release Date : 2019-04-10

Theory And Applications Of Models Of Computation written by T.V. Gopal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-10 with Computers categories.

This book constitutes the refereed proceedings of the 15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019, held in Kitakyushu, Japan, in April 2019. The 43 revised full papers were carefully reviewed and selected from 60 submissions. The main themes of the selected papers are computability, computer science logic, complexity, algorithms, models of computation, and systems theory.

Logic Colloquium 01

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Author : Matthias Baaz
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-30

Logic Colloquium 01 written by Matthias Baaz 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 2017-03-30 with Mathematics categories.

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. This volume, the twentieth publication in the Lecture Notes in Logic series, contains the proceedings of the 2001 European Summer Meeting of the Association for Symbolic Logic, held at the Vienna University of Technology. Two long articles present accessible expositions on resolution theorem proving and the determinacy of long games. The remaining articles cover separate research topics in many areas of mathematical logic, including applications in computer science, proof theory, set theory, model theory, computability theory, linguistics and aspects of philosophy. This collection will interest not only mathematical logicians but also philosophical logicians, historians of logic, computer scientists, formal linguists and mathematicians working in algebra, abstract analysis and topology.

Computable Structures And The Hyperarithmetical Hierarchy

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