LEADER 03154nam 22005415 450 001 9910300124703321 005 20200703073641.0 010 $a3-319-92414-1 024 7 $a10.1007/978-3-319-92414-4 035 $a(CKB)4100000007159017 035 $a(DE-He213)978-3-319-92414-4 035 $a(MiAaPQ)EBC6311983 035 $a(PPN)232471312 035 $a(EXLCZ)994100000007159017 100 $a20181123d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSets, Models and Proofs /$fby Ieke Moerdijk, Jaap van Oosten 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XIV, 141 p. 39 illus.) 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 311 $a3-319-92413-3 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- 1 Sets -- 2 Models -- 3 Proofs -- 4 Sets Again -- Appendix: Topics for Further Study -- Photo Credits -- Bibliography -- Index. 330 $aThis textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel?s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year. 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aProof theory 606 $aAlgebra 606 $aStructures and Proofs$3https://scigraph.springernature.com/ontologies/product-market-codes/M24010 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 615 0$aProof theory. 615 0$aAlgebra. 615 14$aStructures and Proofs. 615 24$aAlgebra. 676 $a511.3 700 $aMoerdijk$b Ieke$4aut$4http://id.loc.gov/vocabulary/relators/aut$059494 702 $avan Oosten$b Jaap$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300124703321 996 $aSets, Models and Proofs$92047132 997 $aUNINA