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:
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Provides a complete introduction to reverse mathematics, including
necessary background from computability theory, second order
arithmetic, forcing, induction, and model construction
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Offers a comprehensive treatment of the reverse mathematics of
combinatorics, including Ramsey's theorem, Hindman's theorem, and many
other results
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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
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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.
