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020			_a9783030738419
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082			_a510.6 _bEBB-M
100			_aEbbinghaus, Heinz-Dieter
245			_aMathematical logic
250			_a3rd ed.
260			_aSwitzerland : _bSpringer Nature, _c2021.
300			_aix, 304p. : _billustrations ; _c25 cm.
490			_aGraduate texts in mathematics, _v291. _x0072-5285;
504			_aIncludes bibliographical references (pages 291-292) and index.
520			_aThis textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science. The chapters are carefully organized, featuring complete proofs and numerous examples throughout. Beginning with motivating examples, the book goes on to present the syntax and semantics of first-order logic. After providing a sequent calculus for this logic, a Henkin-type proof of the completeness theorem is given. These introductory chapters prepare the reader for the advanced topics that follow, such as Gödel's Incompleteness Theorems, Trakhtenbrot's undecidability theorem, Lindström's theorems on the maximality of first-order logic, and results linking logic with automata theory. This new edition features many modernizations, as well as two additional important results: The decidability of Presburger arithmetic, and the decidability of the weak monadic theory of the successor function. Mathematical Logic is ideal for students beginning their studies in logic and the foundations of mathematics. Although the primary audience for this textbook will be graduate students or advanced undergraduates in mathematics or computer science, in fact the book has few formal prerequisites. It demands of the reader only mathematical maturity and experience with basic abstract structures, such as those encountered in discrete mathematics or algebra.
650			_aLogic, Symbolic and mathematical.
650			_aMathematical Logic and Foundations.
650			_aMathematics of Computing.
650			_aPredicate calculus.
650			_aGödel’s completeness theorem
650			_aMathematical provability
650			_aModel theory logic
650			_aTrakhtenbrot’s theorem
650			_aHerbrand's theorem
650			_aLindström’s theorem
650			_aPresburger arithmetic
650			_aModel theory logic
700			_aFlum, Jörg
700			_aThomas, Wolfgang
856			_3Table of contents _uhttps://link.springer.com/content/pdf/bfm:978-3-030-73839-6/1
856			_3Reviews _uhttps://www.goodreads.com/book/show/71365922-mathematical-logic?ref=nav_sb_ss_1_13#CommunityReviews
942			_2udc _cN
999			_c35072 _d35072