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Degrees of Unsolvability

Degrees of Unsolvability
Author: Gerald E. Sacks
Publisher:
Total Pages: 196
Release: 1966
Genre: Mathematics
ISBN:

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The description for this book, Degrees of Unsolvability. (AM-55), Volume 55, will be forthcoming.


Handbook of Mathematical Logic

Handbook of Mathematical Logic
Author: J. Barwise
Publisher: Elsevier
Total Pages: 1179
Release: 1982-03-01
Genre: Computers
ISBN: 0080933645

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The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.


Handbook of Computability Theory

Handbook of Computability Theory
Author: E.R. Griffor
Publisher: Elsevier
Total Pages: 741
Release: 1999-10-01
Genre: Mathematics
ISBN: 0080533043

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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.


The Once and Future Turing

The Once and Future Turing
Author: S. Barry Cooper
Publisher: Cambridge University Press
Total Pages: 398
Release: 2016-03-24
Genre: Mathematics
ISBN: 131658917X

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Alan Turing (1912–1954) made seminal contributions to mathematical logic, computation, computer science, artificial intelligence, cryptography and theoretical biology. In this volume, outstanding scientific thinkers take a fresh look at the great range of Turing's contributions, on how the subjects have developed since his time, and how they might develop still further. The contributors include Martin Davis, J. M. E. Hyland, Andrew R. Booker, Ueli Maurer, Kanti V. Mardia, S. Barry Cooper, Stephen Wolfram, Christof Teuscher, Douglas Richard Hofstadter, Philip K. Maini, Thomas E. Woolley, Eamonn A. Gaffney, Ruth E. Baker, Richard Gordon, Stuart Kauffman, Scott Aaronson, Solomon Feferman, P. D. Welch and Roger Penrose. These specially commissioned essays will provoke and engross the reader who wishes to understand better the lasting significance of one of the twentieth century's deepest thinkers.


Contributions to Mathematical Logic

Contributions to Mathematical Logic
Author: Lev D. Beklemishev
Publisher: Elsevier
Total Pages: 311
Release: 2000-04-01
Genre: Computers
ISBN: 0080957692

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Contributions to Mathematical Logic


Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88
Author: Robion C. Kirby
Publisher: Princeton University Press
Total Pages: 368
Release: 2016-03-02
Genre: Mathematics
ISBN: 1400881501

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Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.


Infinite Loop Spaces (AM-90), Volume 90

Infinite Loop Spaces (AM-90), Volume 90
Author: John Frank Adams
Publisher: Princeton University Press
Total Pages: 230
Release: 1978-09-01
Genre: Mathematics
ISBN: 1400821258

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The theory of infinite loop spaces has been the center of much recent activity in algebraic topology. Frank Adams surveys this extensive work for researchers and students. Among the major topics covered are generalized cohomology theories and spectra; infinite-loop space machines in the sense of Boadman-Vogt, May, and Segal; localization and group completion; the transfer; the Adams conjecture and several proofs of it; and the recent theories of Adams and Priddy and of Madsen, Snaith, and Tornehave.


Computability

Computability
Author: Nigel Cutland
Publisher: Cambridge University Press
Total Pages: 268
Release: 1980-06-19
Genre: Computers
ISBN: 9780521294652

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What can computers do in principle? What are their inherent theoretical limitations? The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function - a function whose values can be calculated in an automatic way.


Contributions to Mathematical Logic

Contributions to Mathematical Logic
Author: H. Arnold Schmidt
Publisher:
Total Pages: 332
Release: 1968
Genre: Logic, Symbolic and mathematical
ISBN:

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Computability Theory and Its Applications

Computability Theory and Its Applications
Author: Peter Cholak
Publisher: American Mathematical Soc.
Total Pages: 338
Release: 2000
Genre: Mathematics
ISBN: 0821819224

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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).