00874nam a2200217 i 4500991000412919707536091023s1986 de 000 0 ger d3596223482 b13853442-39ule_instBurger, Hermann195753Die Allmähliche Verfertigung Der Idee Beim Schreiben :Frankfurter Poetik-Vorlesung /Hermann BurgerFrankfurt am Main :S. Fischer,c1986107 p. ;19 cm.Collection S. Fischer ;bd. 48Burger, HermannPoetica.b1385344202-04-1423-10-09991000412919707536LE012 838.914 BUR 412012000363960le012-E0.00-l- 01310.i1501822223-10-09Allmähliche Verfertigung Der Idee Beim Schreiben228637UNISALENTOle01223-10-09ma -gerde 4004582nam 22006495 450 991058578490332120251113175427.03-031-11367-510.1007/978-3-031-11367-3(MiAaPQ)EBC7050334(Au-PeEL)EBL7050334(CKB)24281725100041(PPN)263898709(OCoLC)1337946026(DE-He213)978-3-031-11367-3(EXLCZ)992428172510004120220725d2022 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierReverse Mathematics Problems, Reductions, and Proofs /by Damir D. Dzhafarov, Carl Mummert1st ed. 2022.Cham :Springer International Publishing :Imprint: Springer,2022.1 online resource (498 pages)Theory and Applications of Computability, In cooperation with the Association Computability in Europe,2190-6203Print version: Dzhafarov, Damir D. Reverse Mathematics Cham : Springer International Publishing AG,c2022 9783031113666 Includes bibliographical references and index.1 introduction -- Part I Computable mathematics: 2 Computability theory -- 3 Instance–solution problems -- 4 Problem reducibilities -- Part II Formalization and syntax: 5 Second order arithmetic -- 6 Induction and bounding -- 7 Forcing -- Part III Combinatorics: 8 Ramsey’s theorem -- 9 Other combinatorial principles -- Part IV Other areas: 10 Analysis and topology -- 11 Algebra -- 12 Set theory and beyond.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.Theory and Applications of Computability, In cooperation with the Association Computability in Europe,2190-6203Computer scienceMathematicsComputable functionsRecursion theoryLogic, Symbolic and mathematicalMathematics of ComputingComputability and Recursion TheoryMathematical Logic and FoundationsComputer scienceMathematics.Computable functions.Recursion theory.Logic, Symbolic and mathematical.Mathematics of Computing.Computability and Recursion Theory.Mathematical Logic and Foundations.511.3511.3Dzhafarov Damir D.1252240Mummert Carl1978-MiAaPQMiAaPQMiAaPQBOOK9910585784903321Reverse mathematics2999664UNINA