LEADER 04196nam 22006855 450 001 9910438150503321 005 20200706132557.0 010 $a1-4614-5746-7 024 7 $a10.1007/978-1-4614-5746-6 035 $a(CKB)2670000000340828 035 $a(EBL)1081993 035 $a(OCoLC)827212490 035 $a(SSID)ssj0000878683 035 $a(PQKBManifestationID)11465384 035 $a(PQKBTitleCode)TC0000878683 035 $a(PQKBWorkID)10837170 035 $a(PQKB)10682300 035 $a(DE-He213)978-1-4614-5746-6 035 $a(MiAaPQ)EBC6313059 035 $a(MiAaPQ)EBC1081993 035 $a(Au-PeEL)EBL1081993 035 $a(CaPaEBR)ebr10983245 035 $a(PPN)168303809 035 $a(EXLCZ)992670000000340828 100 $a20130125d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA Course on Mathematical Logic /$fby Shashi Mohan Srivastava 205 $a2nd ed. 2013. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013. 215 $a1 online resource (206 p.) 225 1 $aUniversitext,$x0172-5939 300 $aDescription based upon print version of record. 311 $a1-4614-5745-9 320 $aIncludes bibliographical references and index. 327 $aPreface -- 1 Syntax of First-Order Logic -- 2 Semantics of First-Order Languages -- 3 Propositional Logic -- 4 Completeness Theorem for First-Order Logic -- 5 Model Theory -- 6 Recursive Functions and Arithmetization of Theories -- 7 Incompleteness Theorems and Recursion Theory -- References -- Index. 330 $aThis is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel?s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more. Review from the first edition: "All results included in the book are very carefully selected and proved. The author?s manner of writing is excellent, which will surely make this book useful to many categories of readers." --Marius Tarnauceanu, Zentralblatt MATH. 410 0$aUniversitext,$x0172-5939 606 $aMathematical logic 606 $aAlgebra 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 606 $aMathematical Logic and Formal Languages$3https://scigraph.springernature.com/ontologies/product-market-codes/I16048 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 615 0$aMathematical logic. 615 0$aAlgebra. 615 14$aMathematical Logic and Foundations. 615 24$aMathematical Logic and Formal Languages. 615 24$aAlgebra. 676 $a511.3 700 $aSrivastava$b Shashi Mohan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0521449 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438150503321 996 $aCourse on mathematical logic$9836919 997 $aUNINA