LEADER 04181nam 22005295 450 001 9910855373203321 005 20251027100250.0 010 $a3-031-55368-3 024 7 $a10.1007/978-3-031-55368-4 035 $a(CKB)31988353800041 035 $a(MiAaPQ)EBC31326003 035 $a(Au-PeEL)EBL31326003 035 $a(MiAaPQ)EBC31322972 035 $a(Au-PeEL)EBL31322972 035 $a(DE-He213)978-3-031-55368-4 035 $a(EXLCZ)9931988353800041 100 $a20240506d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn Invitation to Mathematical Logic /$fby David Marker 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (359 pages) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v301 311 08$a3-031-55367-5 327 $aIntroduction -- I. Truth and Proof -- 1 Languages, Structures and Theories -- 2 Embeddings and Substructures -- 3 Formal Proofs -- 4 Gödel's Completeness Theorem -- II. Elements of Model Theory -- 5 Compactness and Complete Theories -- 6 Ultraproducts -- 7 Quantifier Elimination -- 8 Model Theory of the Real Field -- III. Computability -- 9 Models of Computation -- 10 Universal Machines and Undecidability -- 11 Computably Enumerable and Arithmetic Sets -- 12 Turing Reducibility -- IV. Arithmetic and Incompleteness.-13 Gödel's Incompleteness Theorems -- 14 Hilbert?s 10th Problem -- 15 Peano Arithmetic and ?0 -- 16 Models of Arithmetic and Independence Results. - Appendices -- A Set Theory. - B Unique Readability. - C Real Algebra. -Bibliography. - Index. 330 $aIn addition to covering the essentials, the author?s intention in writing this text is to entice the reader to further study mathematical logic. There is no current ?standard text? for a first graduate course in mathematical logic and this book will fill that gap. While there is more material than could be covered in a traditional one semester course, an instructor can cover the basics and still have the flexibility to choose several weeks? worth of interesting advanced topics that have been introduced. The text can and will be used by people in various courses with different sorts of perspectives. This versatility is one of the many appealing aspects of this book. A list of suggested portions to be covered in a single course is provided as well as a useful chart which maps chapter dependencies. Additionally, a motivated student will have ample material for further reading. New definitions, formalism, and syntax have been streamlined to engage the reader quickly into the heart of logic and to more sophisticated topics. Part I and Part IV center on foundational questions, while Part III establishes the fundamentals of computability. Part II develops model theory, highlighting the model theory of the fields of real and complex numbers. The interplay between logic and other areas of mathematics, notably algebra, number theory, and combinatorics, are illustrated in Chapters 5, 6, 8, 14, and 16. For most of the text, the only prerequisite is mathematical maturity. The material should be accessible to first year graduate students or advanced undergraduates in mathematics, graduate students in philosophy with a solid math background, or students in computer science who want a mathematical introduction to logic. Prior exposure to logic is helpful but not assumed. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v301 606 $aLogic, Symbolic and mathematical 606 $aMathematical Logic and Foundations 606 $aLògica matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aLogic, Symbolic and mathematical. 615 14$aMathematical Logic and Foundations. 615 7$aLògica matemàtica 676 $a511.3 700 $aMarker$b David$066978 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910855373203321 996 $aInvitation to Mathematical Logic$94299915 997 $aUNINA