LEADER 04261nam 22006375 450 001 9910483447003321 005 20240206135607.0 010 $a3-030-73839-6 024 7 $a10.1007/978-3-030-73839-6 035 $a(CKB)4100000011946754 035 $a(MiAaPQ)EBC6632537 035 $a(Au-PeEL)EBL6632537 035 $a(OCoLC)1253630465 035 $a(DE-He213)978-3-030-73839-6 035 $a(PPN)255881959 035 $a(EXLCZ)994100000011946754 100 $a20210528d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical Logic /$fby Heinz-Dieter Ebbinghaus, Jörg Flum, Wolfgang Thomas 205 $a3rd ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (305 pages) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v291 311 $a3-030-73838-8 320 $aIncludes bibliographical references and index. 327 $aA -- I Introduction -- II Syntax of First-Order Languages -- III Semantics of First-Order Languages -- IV A Sequent Calculus -- V The Completeness Theorem -- VI The Löwenheim?Skolem and the Compactness Theorem -- VII The Scope of First-Order Logic -- VIII Syntactic Interpretations and Normal Forms -- B -- IX Extensions of First-Order Logic -- X Computability and Its Limitations -- XI Free Models and Logic Programming -- XII An Algebraic Characterization of Elementary Equivalence -- XIII Lindström?s Theorems -- References -- List of Symbols -- Subject Index. 330 $aThis textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science. The chapters are carefully organized, featuring complete proofs and numerous examples throughout. Beginning with motivating examples, the book goes on to present the syntax and semantics of first-order logic. After providing a sequent calculus for this logic, a Henkin-type proof of the completeness theorem is given. These introductory chapters prepare the reader for the advanced topics that follow, such as Gödel's Incompleteness Theorems, Trakhtenbrot's undecidability theorem, Lindström's theorems on the maximality of first-order logic, and results linking logic with automata theory. This new edition features many modernizations, as well as two additional important results: The decidability of Presburger arithmetic, and the decidability of the weak monadic theory of the successor function. Mathematical Logic is ideal for students beginning their studies in logic and the foundations of mathematics. Although the primary audience for this textbook will be graduate students or advanced undergraduates in mathematics or computer science, in fact the book has few formal prerequisites. It demands of the reader only mathematical maturity and experience with basic abstract structures, such as those encountered in discrete mathematics or algebra. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v291 606 $aMathematical logic 606 $aComputer science$xMathematics 606 $aMathematical Logic and Foundations 606 $aMathematics of Computing 606 $aCàlcul$2thub 606 $aLògica matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematical logic. 615 0$aComputer science$xMathematics. 615 14$aMathematical Logic and Foundations. 615 24$aMathematics of Computing. 615 7$aCàlcul 615 7$aLògica matemàtica 676 $a511.3 700 $aEbbinghaus$b Heinz-Dieter$f1939-$01068399 702 $aFlum$b Jo?rg 702 $aThomas$b Wolfgang$f1947- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483447003321 996 $aMathematical logic$92553144 997 $aUNINA