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001 978-3-642-31933-4
003 DE-He213
005 20200421112548.0
007 cr nn 008mamaa
008 160620s2016 gw | s |||| 0|eng d
020 _a9783642319334
_9978-3-642-31933-4
024 7 _a10.1007/978-3-642-31933-4
_2doi
050 4 _aQA75.5-76.95
072 7 _aUY
_2bicssc
072 7 _aUYA
_2bicssc
072 7 _aCOM014000
_2bisacsh
072 7 _aCOM031000
_2bisacsh
082 0 4 _a004.0151
_223
100 1 _aSoare, Robert I.
_eauthor.
245 1 0 _aTuring Computability
_h[electronic resource] :
_bTheory and Applications /
_cby Robert I. Soare.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2016.
300 _aXXXVI, 263 p. 4 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _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 (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 _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.
650 0 _aComputer science.
650 0 _aComputers.
650 0 _aComputer science
_xMathematics.
650 0 _aMathematical logic.
650 1 4 _aComputer Science.
650 2 4 _aTheory of Computation.
650 2 4 _aMathematics of Computing.
650 2 4 _aMathematical Logic and Foundations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642319327
830 0 _aTheory and Applications of Computability, In cooperation with the association Computability in Europe,
_x2190-619X
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-31933-4
912 _aZDB-2-SCS
942 _cEBK
999 _c58719
_d58719