Constructibility


Author: Keith J. Devlin
Publisher: Cambridge University Press
ISBN: 110716835X
Category: Computers
Page: 437
View: 5958
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A comprehensive account of the theory of constructible sets at an advanced level, aimed at graduate mathematicians.

Computability in Context

Computation and Logic in the Real World
Author: S Barry Cooper,Andrea Sorbi
Publisher: World Scientific
ISBN: 1908978767
Category: Mathematics
Page: 420
View: 412
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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. Contents:Computation, Information, and the Arrow of Time (P Adriaans & P van Emde Boas)The Isomorphism Conjecture for NP (M Agrawal)The Ershov Hierarchy (M M Arslanov)Complexity and Approximation in Reoptimization (G Ausiello et al.)Definability in the Real Universe (S B Cooper)HF-Computability (Y L Drshov et al.)The Mathematics of Computing Between Logic and Physics (G Longo & T Paul)Liquid State Machines: Motivation, Theory, and Applications (W Maass)Experiments on an Internal Approach to Typed Algorithms in Analysis (D Normann)Recursive Functions: An Archeological Look (P Odifreddi)Reverse Mathematics and Well-Ordering Principles (M Rathjen & A Weiermann)Discrete Transfinite Computation Models (P D Welch) Readership: Researchers in computational mathematics, logic, and theoretical computer science. Keywords:Computability;Logic;Real World;Turing Barrier;Real Computation;Learning Theory

Constructibility


Author: Keith J. Devlin
Publisher: Springer Verlag
ISBN: 9783540132585
Category: Mathematics
Page: 425
View: 2224
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Logic Colloquium 2005


Author: Costas Dimitracopoulos
Publisher: Cambridge University Press
ISBN: 052188425X
Category: Computers
Page: 272
View: 838
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This 2007 volume includes surveys, tutorials, and selected research papers on advances in logic.

Fundamentals of Mathematical Logic


Author: Peter G. Hinman
Publisher: CRC Press
ISBN: 1439864276
Category: Mathematics
Page: 896
View: 4567
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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.

Recursion Theory

Computational Aspects of Definability
Author: Chi Tat Chong,Liang Yu
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110275643
Category: Mathematics
Page: 320
View: 4847
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This monograph presents recursion theory from a generalized and largely global point of view. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using ideas and techniques beyond those of classical recursion theory. These include structure theory, hyperarithmetic determinacy and rigidity, basis theorems, independence results on Turing degrees, as well as applications to higher randomness.

Days in logic '06

two tutorials
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: 78
View: 1020
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International Books in Print


Author: N.A
Publisher: N.A
ISBN: 9783598221187
Category: English imprints
Page: 5
View: 7398
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Admissible Sets and Structures


Author: Jon Barwise
Publisher: Cambridge University Press
ISBN: 1316739414
Category: Mathematics
Page: N.A
View: 2789
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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. Admissible set theory is a major source of interaction between model theory, recursion theory and set theory, and plays an important role in definability theory. In this volume, the seventh publication in the Perspectives in Logic series, Jon Barwise presents the basic facts about admissible sets and admissible ordinals in a way that makes them accessible to logic students and specialists alike. It fills the artificial gap between model theory and recursion theory and covers everything the logician should know about admissible sets.

Higher Recursion Theory


Author: Gerald E. Sacks
Publisher: Cambridge University Press
ISBN: 1107168430
Category: Mathematics
Page: 360
View: 9594
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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 second publication in the Perspectives in Logic series, is an almost self-contained introduction to higher recursion theory, in which the reader is only assumed to know the basics of classical recursion theory. The book is divided into four parts: hyperarithmetic sets, metarecursion, α-recursion, and E-recursion. This text is essential reading for all researchers in the field.

The Bulletin of Symbolic Logic


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Logic, Symbolic and mathematical
Page: N.A
View: 4267
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Subject Guide to Books in Print


Author: N.A
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
View: 6467
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Publicationes mathematicae


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 8537
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Intermediate set theory


Author: Frank Robert Drake,Dasharath Singh
Publisher: John Wiley & Sons Inc
ISBN: 9780471964940
Category: Mathematics
Page: 234
View: 328
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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.

L'Enseignement mathématique


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 1241
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Vols. for 1965- include a separately paged section, Bulletin bibliographique.

The Mathematical Intelligencer


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 879
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Computability in Analysis and Physics


Author: Marian B. Pour-El,J. Ian Richards
Publisher: Cambridge University Press
ISBN: 1107168449
Category: Mathematics
Page: 218
View: 8789
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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 this volume, the first publication in the Perspectives in Logic series, Pour-El and Richards present the first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning. The book focuses on the computability or noncomputability of standard processes in analysis and physics. Topics include classical analysis, Hilbert and Banach spaces, bounded and unbounded linear operators, eigenvalues, eigenvectors, and equations of mathematical physics. The work is self-contained, and although it is intended primarily for logicians and analysts, it should also be of interest to researchers and graduate students in physics and computer science.

Model-Theoretic Logics


Author: J. Barwise,S. Feferman
Publisher: Cambridge University Press
ISBN: 1316739392
Category: Mathematics
Page: N.A
View: 5544
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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 eighth publication in the Perspectives in Logic series, brings together several directions of work in model theory between the late 1950s and early 1980s. It contains expository papers by pre-eminent researchers. Part I provides an introduction to the subject as a whole, as well as to the basic theory and examples. The rest of the book addresses finitary languages with additional quantifiers, infinitary languages, second-order logic, logics of topology and analysis, and advanced topics in abstract model theory. Many chapters can be read independently.

The higher infinite

large cardinals in set theory from their beginnings
Author: Akihiro Kanamori
Publisher: Springer
ISBN: N.A
Category: Mathematics
Page: 536
View: 6443
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Metamathematics of First-Order Arithmetic


Author: Petr Hájek,Pavel Pudlák
Publisher: Cambridge University Press
ISBN: 1316739457
Category: Mathematics
Page: N.A
View: 2098
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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 third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).