Author: Keith J. Devlin

Publisher: Cambridge University Press

ISBN: 110716835X

Category: Computers

Page: 437

View: 2045

A comprehensive account of the theory of constructible sets at an advanced level, aimed at graduate mathematicians.

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A comprehensive account of the theory of constructible sets at an advanced level, aimed at graduate mathematicians.

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This book constitutes the refereed proceedings of the 7th Conference on Computability in Europe, CiE 2011, held in Sofia, Bulgaria, in June/July 2011. The 22 revised papers presented together with 11 invited lectures were carefully reviewed and selected with an acceptance rate of under 40%. The papers cover the topics computability in analysis, algebra, and geometry; classical computability theory; natural computing; relations between the physical world and formal models of computability; theory of transfinite computations; and computational linguistics.

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For over half a century, Boris (Boaz) Trakhtenbrot has made seminal contributions to virtually all of the central areas of theoretical computer science. This festschrift volume readily illustrates the profound influence he has had on the field.

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This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

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The authors cover first order logic and the main topics of set theory in a clear mathematical style with sensible philosophical discussion. The emphasis is on presenting the use of set theory in various areas of mathematics, with particular attention paid to introducing axiomatic set theory, showing how the axioms are needed in mathematical practice and how they arise. Other areas introduced include the axiom of choice, filters and ideals. Exercises are provided which are suitable for both beginning students and degree-level students.

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This book is a text of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last 10 to 15 years, including the independence of the continuum hypothesis, the Diophantine nature of enumerable sets and the impossibility of finding an algorithmic solution for certain problems. The book contains the first textbook presentation of Matijasevic's result. The central notions are provability and computability; the emphasis of the presentation is on aspects of the theory which are of interest to the working mathematician. Many of the approaches and topics covered are not standard parts of logic courses; they include a discussion of the logic of quantum mechanics, Goedel's constructible sets as a sub-class of von Neumann's universe, the Kolmogorov theory of complexity. Feferman's theorem on Goedel formulas as axioms and Highman's theorem on groups defined by enumerable sets of generators and relations. A number of informal digressions concerned with psychology, linguistics, and common sense logic should interest students of the philosophy of science or the humanities.

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This volume has its origin in a meeting that was held in Santiago de Compostela University, Santiago de Compostela (Spain) in January 1996. The meeting was organized by the Department of Logic and Philosophy of Science in cooperation with the Association for Logic, Methodology and Philosophy of Science in Spain.Within analytical philosophy issues such as the definability of truth, its semantic relevance, its role in the distinction between formal and natural languages, the status of truth-bearers or in its case of truth-makers, have become a crossroads in the studies of logic, philosophy of science, philosophy of language, philosophy of mind, epistemology and ontology. Thus, in spite of what the title Truth in Perspective may suggest to the reader at first, the present volume is not only - though it is also - a presentation of different theories or conceptions of truth. Most of the book presents a vision of different groups of philosophical questions in which the issue of truth appears embedded together with other related themes, from different points of view.

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This volume makes the basic facts about admissible sets accessible to logic students and specialists alike.

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Author: Keith J. Devlin

Publisher: Cambridge University Press

ISBN: 110716835X

Category: Computers

Page: 437

View: 2045

A comprehensive account of the theory of constructible sets at an advanced level, aimed at graduate mathematicians.

*7th Conference on Computability in Europe, CiE 2011, Sofia, Bulgaria, June 27 - July 2, 2011, Proceedings*

Author: Benedikt Löwe,Dag Normann,Ivan Soskov,Alexandra Soskova

Publisher: Springer Science & Business Media

ISBN: 3642218741

Category: Computers

Page: 319

View: 2681

This book constitutes the refereed proceedings of the 7th Conference on Computability in Europe, CiE 2011, held in Sofia, Bulgaria, in June/July 2011. The 22 revised papers presented together with 11 invited lectures were carefully reviewed and selected with an acceptance rate of under 40%. The papers cover the topics computability in analysis, algebra, and geometry; classical computability theory; natural computing; relations between the physical world and formal models of computability; theory of transfinite computations; and computational linguistics.

*Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday*

Author: Arnon Avron,Nachum Dershowitz,Alexander Rabinovich

Publisher: Springer

ISBN: 3540781277

Category: Computers

Page: 683

View: 5257

For over half a century, Boris (Boaz) Trakhtenbrot has made seminal contributions to virtually all of the central areas of theoretical computer science. This festschrift volume readily illustrates the profound influence he has had on the field.

*two tutorials*

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 78

View: 6903

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: N.A

View: 4508

Author: Peter G. Hinman

Publisher: A K Peters/CRC Press

ISBN: 9781568812625

Category: Mathematics

Page: 896

View: 5178

This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

Author: N.A

Publisher: N.A

ISBN: 9783598221187

Category: English imprints

Page: 5

View: 8199

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

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Author: Frank Robert Drake,Dasharath Singh

Publisher: John Wiley & Sons Inc

ISBN: 9780471964940

Category: Mathematics

Page: 234

View: 3305

The authors cover first order logic and the main topics of set theory in a clear mathematical style with sensible philosophical discussion. The emphasis is on presenting the use of set theory in various areas of mathematics, with particular attention paid to introducing axiomatic set theory, showing how the axioms are needed in mathematical practice and how they arise. Other areas introduced include the axiom of choice, filters and ideals. Exercises are provided which are suitable for both beginning students and degree-level students.

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2521

Author: I͡U. I. Manin,Jurij I. Manin,Yu I. Manin,︠I︡U. I. Manin,I︠U︡riĭ Ivanovich Manin,Ûrij Ivanovič Manin

Publisher: Springer Science & Business Media

ISBN: 9780387902432

Category: Mathematics

Page: 286

View: 3775

This book is a text of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last 10 to 15 years, including the independence of the continuum hypothesis, the Diophantine nature of enumerable sets and the impossibility of finding an algorithmic solution for certain problems. The book contains the first textbook presentation of Matijasevic's result. The central notions are provability and computability; the emphasis of the presentation is on aspects of the theory which are of interest to the working mathematician. Many of the approaches and topics covered are not standard parts of logic courses; they include a discussion of the logic of quantum mechanics, Goedel's constructible sets as a sub-class of von Neumann's universe, the Kolmogorov theory of complexity. Feferman's theorem on Goedel formulas as axioms and Highman's theorem on groups defined by enumerable sets of generators and relations. A number of informal digressions concerned with psychology, linguistics, and common sense logic should interest students of the philosophy of science or the humanities.

*Mathematica. Dissertationes*

Author: N.A

Publisher: N.A

ISBN: 9789514107924

Category: Mathematics

Page: 71

View: 4722

*recent issues in logic, representation and ontology*

Author: Concha Martínez,Uxía Rivas,Luis Villegas-Forero

Publisher: Avebury

ISBN: 9781859726983

Category: Philosophy

Page: 417

View: 8546

This volume has its origin in a meeting that was held in Santiago de Compostela University, Santiago de Compostela (Spain) in January 1996. The meeting was organized by the Department of Logic and Philosophy of Science in cooperation with the Association for Logic, Methodology and Philosophy of Science in Spain.Within analytical philosophy issues such as the definability of truth, its semantic relevance, its role in the distinction between formal and natural languages, the status of truth-bearers or in its case of truth-makers, have become a crossroads in the studies of logic, philosophy of science, philosophy of language, philosophy of mind, epistemology and ontology. Thus, in spite of what the title Truth in Perspective may suggest to the reader at first, the present volume is not only - though it is also - a presentation of different theories or conceptions of truth. Most of the book presents a vision of different groups of philosophical questions in which the issue of truth appears embedded together with other related themes, from different points of view.

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematical reviews

Page: N.A

View: 6838

Author: Jon Barwise

Publisher: Cambridge University Press

ISBN: 1107168333

Category: Mathematics

Page: 408

View: 2328

This volume makes the basic facts about admissible sets accessible to logic students and specialists alike.

*Widerspruchsfreiheit und Unabhängigkeit der Kontinuum-Hypothese und des Auswahlaxioms*

Author: R. B. Jensen

Publisher: Springer-Verlag

ISBN: 3540349766

Category: Mathematics

Page: 178

View: 9318