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Reverse Mathematics
Damir D. Dzhafarov, Carl Mummert (Gebundene Ausgabe, Englisch)
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Beschreibung
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 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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
26.07.2022
Sprache
Englisch
EAN
9783031113666
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Theory and Applications of Computability
Sonderedition
Nein
Autor
Damir D. Dzhafarov, Carl Mummert
Seitenanzahl
488
Einbandart
Gebundene Ausgabe
Buch Untertitel
Problems, Reductions, and Proofs
Schlagwörter
Reverse mathematics, Computability theory, Second-order arithmetic, Continuous mathematics, Sequence coding
Thema-Inhalt
UYAM - Mathematik für Informatiker
PBCD - Mathematik: Logik
PBC - Mathematische Grundlagen
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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