Reverse Mathematics
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Reverse Mathematics
Author: Damir D. Dzhafarov
language: en
Publisher: Springer Nature
Release Date: 2022-07-25
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.
Reverse Mathematics
Author: John Stillwell
language: en
Publisher: Princeton University Press
Release Date: 2019-09-24
This volume presents reverse mathematics to a general mathematical audience for the first time. Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. to logic.
Reverse Mathematics 2001
Author: Stephen G. Simpson
language: en
Publisher: Cambridge University Press
Release Date: 2017-03-30
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Reverse mathematics is a program of research in the foundations of mathematics, motivated by two foundational questions: 'what are appropriate axioms for mathematics?' and 'what are the logical strengths of particular axioms and particular theorems?' This volume, the twenty-first publication in the Lecture Notes in Logic series, contains twenty-four original research papers from respected authors that present exciting new developments in reverse mathematics and subsystems of second order arithmetic since 1998.