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001 978-3-031-11367-3
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020 _a9783031113673
_9978-3-031-11367-3
024 7 _a10.1007/978-3-031-11367-3
_2doi
050 4 _aQA76.9.M35
072 7 _aUYAM
_2bicssc
072 7 _aCOM014000
_2bisacsh
072 7 _aUYAM
_2thema
082 0 4 _a004.0151
_223
100 1 _aDzhafarov, Damir D.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aReverse Mathematics
_h[electronic resource] :
_bProblems, Reductions, and Proofs /
_cby Damir D. Dzhafarov, Carl Mummert.
250 _a1st ed. 2022.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2022.
300 _aXIX, 488 p. 1 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,
_x2190-6203
505 0 _a1 introduction -- Part I Computable mathematics: 2 Computability theory -- 3 Instance–solution problems -- 4 Problem reducibilities -- Part II Formalization and syntax: 5 Second order arithmetic -- 6 Induction and bounding -- 7 Forcing -- Part III Combinatorics: 8 Ramsey’s theorem -- 9 Other combinatorial principles -- Part IV Other areas: 10 Analysis and topology -- 11 Algebra -- 12 Set theory and beyond.
520 _aReverse mathematics studies the complexity of proving mathematical theorems and solving mathematical problems. Typical questions include: Can we prove this result without first proving that one? Can a computer solve this problem? A highly active part of mathematical logic and computability theory, the subject offers beautiful results as well as significant foundational insights. This text provides a modern treatment of reverse mathematics that combines computability theoretic reductions and proofs in formal arithmetic to measure the complexity of theorems and problems from all areas of mathematics. It includes detailed introductions to techniques from computable mathematics, Weihrauch style analysis, and other parts of computability that have become integral to research in the field. Topics and features: Provides a complete introduction to reverse mathematics, including necessary background from computability theory, second order arithmetic, forcing, induction, and model construction Offers a comprehensive treatment of the reverse mathematics of combinatorics, including Ramsey's theorem, Hindman's theorem, and many other results Provides central results and methods from the past two decades, appearing in book form for the first time and including preservation techniques and applications of probabilistic arguments Includes a large number of exercises of varying levels of difficulty, supplementing each chapter The text will be accessible to students with a standard first year course in mathematical logic. It will also be a useful reference for researchers in reverse mathematics, computability theory, proof theory, and related areas. Damir D. Dzhafarov is an Associate Professor of Mathematics at the University of Connecticut, CT, USA. Carl Mummert is a Professor of Computer and Information Technology at Marshall University, WV, USA.
650 0 _aComputer science
_xMathematics.
650 0 _aComputable functions.
650 0 _aRecursion theory.
650 0 _aMathematical logic.
650 1 4 _aMathematics of Computing.
650 2 4 _aComputability and Recursion Theory.
650 2 4 _aMathematical Logic and Foundations.
700 1 _aMummert, Carl.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031113666
776 0 8 _iPrinted edition:
_z9783031113680
776 0 8 _iPrinted edition:
_z9783031113697
830 0 _aTheory and Applications of Computability, In cooperation with the association Computability in Europe,
_x2190-6203
856 4 0 _uhttps://doi.org/10.1007/978-3-031-11367-3
912 _aZDB-2-SCS
912 _aZDB-2-SXCS
942 _cSPRINGER
999 _c177519
_d177519