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Titlebook: Reverse Mathematics; Problems, Reductions Damir D. Dzhafarov,Carl Mummert Textbook 2022 The Editor(s) (if applicable) and The Author(s), un

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書目名稱Reverse Mathematics
副標(biāo)題Problems, Reductions
編輯Damir D. Dzhafarov,Carl Mummert
視頻videohttp://file.papertrans.cn/830/829395/829395.mp4
概述Offers a comprehensive treatment of the reverse mathematics of combinatorics.Includes a large number of exercises of varying levels of difficulty, supplementing each chapter.Provides central results a
叢書名稱Theory and Applications of Computability
圖書封面Titlebook: Reverse Mathematics; Problems, Reductions Damir D. Dzhafarov,Carl Mummert Textbook 2022 The Editor(s) (if applicable) and The Author(s), un
描述.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
出版日期Textbook 2022
關(guān)鍵詞Reverse mathematics; Computability theory; Second-order arithmetic; Continuous mathematics; Sequence cod
版次1
doihttps://doi.org/10.1007/978-3-031-11367-3
isbn_softcover978-3-031-11369-7
isbn_ebook978-3-031-11367-3Series ISSN 2190-619X Series E-ISSN 2190-6203
issn_series 2190-619X
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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Second order arithmetic if we temporarily assume as an axiom that a problem P is solvable, how difficult is it to . that a second problem Q is solvable? If we can prove that Q is solvable under the assumption that P is solvable, this gives us information that Q is “weaker” than P, at least modulo the other axioms used in
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Set theory and beyond”.We cannot easily talk about . (equivalence classes of well orderings) as such in Z., but many properties of the ordinals can be formulated in terms of specific well orderings instead. We have already seen that ATR. can express many such properties quite naturally. In this chapter, we investigate a
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Problem reducibilitiesr does not, then we may view the latter as “harder” from a certain computational standpoint. But it is not obvious how to find such a class for a particular pair of problems, or whether such a class even exists. It is also unclear what relationship this kind of classification really expresses.
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