Turing Computability (Record no. 58719)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04464nam a22005175i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-642-31933-4 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200421112548.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 160620s2016 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783642319334 |
| -- | 978-3-642-31933-4 |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 004.0151 |
| 100 1# - AUTHOR NAME | |
| Author | Soare, Robert I. |
| 245 10 - TITLE STATEMENT | |
| Title | Turing Computability |
| Sub Title | Theory and Applications / |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | XXXVI, 263 p. 4 illus. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Theory and Applications of Computability, In cooperation with the association Computability in Europe, |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | Part I Foundations of Computability -- Chap. 1 Defining Computability -- Chap. 2 Computably Enumerable Sets -- Chap. 3 Turing Reducibility -- Chap. 4 The Arithmetical Hierarchy -- Chap. 5 Classifying C.E. Sets -- Chap. 6 Oracle Constructions and Forcing -- Chap. 7 The Finite Injury Method -- Part II Trees and (SS(B01 Classes -- Chap. 8 Open and Closed Classes -- Chap. 9 Basis Theorems -- Chap. 10 Peano Arithmetic and (SS(B01-Classes -- Chap. 11 Randomness and (SS(B01-Classes -- Part III Minimal Degrees -- Chap. 12 Minimal Degrees Below ��� -- Chap. 13 Minimal Degrees Below �� -- Part IV Games in Computability Theory -- Chap. 14 Banach-Mazur Games -- Chap. 15 Gale-Stewart Games -- Chap. 16 More Lachlan Games -- Part V History of Computability -- Chap. 17 History of Computability -- References -- Index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | Turing's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic. The author presents the subject as an art to be practiced, and an art in the aesthetic sense of inherent beauty which all mathematicians recognize in their subject. Part I gives a thorough development of the foundations of computability, from the definition of Turing machines up to finite injury priority arguments. Key topics include relative computability, and computably enumerable sets, those which can be effectively listed but not necessarily effectively decided, such as the theorems of Peano arithmetic. Part II includes the study of computably open and closed sets of reals and basis and nonbasis theorems for effectively closed sets. Part III covers minimal Turing degrees. Part IV is an introduction to games and their use in proving theorems. Finally, Part V offers a short history of computability theory. The author is a leading authority on the topic and he has taught the subject using the book content over decades, honing it according to experience and feedback from students, lecturers, and researchers around the world. Most chapters include exercises, and the material is carefully structured according to importance and difficulty. The book is suitable for advanced undergraduate and graduate students in computer science and mathematics and researchers engaged with computability and mathematical logic. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| General subdivision | Mathematics. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/978-3-642-31933-4 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 264 #1 - | |
| -- | Berlin, Heidelberg : |
| -- | Springer Berlin Heidelberg : |
| -- | Imprint: Springer, |
| -- | 2016. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer science. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computers. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer science |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematical logic. |
| 650 14 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer Science. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Theory of Computation. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematics of Computing. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematical Logic and Foundations. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| -- | 2190-619X |
| 912 ## - | |
| -- | ZDB-2-SCS |
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