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008			160620s2016 gw | s |||| 0|eng d
020			_a9783642319334
040			_aES-MaUEC
050		4	_aQA9.59 _bS637 2016
082	0	4	_a004.0151
100	1		_aSoare, Robert I. _9100077 _0Local
245	1	0	_aTuring Computability : _bTheory and Applications _cby Robert I Soare
260			_aBerlin, Heidelberg _bSpringer Berlin Heidelberg _c2016
300			_a1 recurso en línea (XXXVI, 263 páginas) _b4 ilustraciones
336			_aTexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
490	0		_aTheory and Applications of Computability, In cooperation with the association Computability in Europe _x2190-619X
505	0		_aPart 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 S01 Classes -- Chap. 8 Open and Closed Classes -- Chap. 9 Basis Theorems -- Chap. 10 Peano Arithmetic and S01-Classes -- Chap. 11 Randomness and S01-Classes -- Part III Minimal Degrees -- Chap. 12 Minimal Degrees Below Øʹʹ -- Chap. 13 Minimal Degrees Below Øʹ -- 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	3		_aTuring'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.
710	2		_aSpringerLink (Online service) _0Local _9106996
942			_2lcc _cLE
988			_aEBOOK, asignarmaterias , EBSPRINGER
650	0	7	_aOrdenadores _0 _2embne _9138111
650		7	_aAgentes inteligentes (Programas de ordenador) _0(OCoLC)1159286 _2embne _0 _9160930
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://link.springer.com/book/10.1007/978-3-642-31933-4 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
901			_ai9783642319334
907			_a.b12956661 _b10-10-17 _c21-11-16
998			_am _a_alco _a_vill _b - - _cm _dz _e- _feng _ggw _h0
945			_aQA9.59 S637 2016 EB _g1 _ieBOOK _j0 _lmae _o- _pEUR0.00 _q- _r- _sb _t15 _u0 _v0 _w0 _x0 _y.i11598505 _z06-04-17
999			_c86388 _d86388 _x1