Name: Reverse Mathematics: Problems, Reductions, and Proofs
Price: 44.45 EUR
Availability: InStock
Author: Dzhafarov, Damir D. ; Mummert, Carl
ISBN: 9783031113697

portada Reverse Mathematics: Problems, Reductions, and Proofs

Reverse Mathematics: Problems, Reductions, and Proofs

Type

Physical Book

Author

Damir D. Dzhafarov

Carl Mummert

Publisher

Springer

Language

English

Pages

488

Format

Paperback

Dimensions

23.4 x 15.6 x 2.6 cm

Weight

0.71 kg.

ISBN13

9783031113697

Synopsis "Reverse Mathematics: Problems, Reductions, and Proofs"

Reverse 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 constructionOffers a comprehensive treatment of the reverse mathematics of combinatorics, including Ramsey's theorem, Hindman's theorem, and many other resultsProvides 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 argumentsIncludes a large number of exercises of varying levels of difficulty, supplementing each chapterThe 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.

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Reverse Mathematics: Problems, Reductions, and Proofs - Dzhafarov, Damir D. ; Mummert, Carl

Synopsis "Reverse Mathematics: Problems, Reductions, and Proofs"

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