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001			394797
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008			220725s2022 sz | s |||| 0|eng d
020			_a9783031113673
024	7		_a10.1007/978-3-031-11367-3 _2doi
040			_aES-MaUEC _bspa _cES-MaUEC
100	1		_aDzhafarov, Damir D _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut
245	1	0	_aReverse Mathematics _bProblems, Reductions, and Proofs _cby Damir D Dzhafarov, Carl Mummert
250			_a1st edition 2022
264		1	_aCham _bSpringer International Publishing _c2022
300			_a1 recurso en línea (XIX, 488 páginas) _b1 illus
336			_atexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
347			_aarchivo de texto _bPDF
490	0		_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.
700	1		_aMummert, Carl _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut
776	0	8	_iPrinted edition: _z9783031113666
776	0	8	_iPrinted edition: _z9783031113680
776	0	8	_iPrinted edition: _z9783031113697
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-031-11367-3 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
988			_aSpringer_Computer_2022
999			_c394797 _d394797