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001 978-1-4614-5746-6
003 DE-He213
005 20140220082821.0
007 cr nn 008mamaa
008 130125s2013 xxu| s |||| 0|eng d
020 _a9781461457466
_9978-1-4614-5746-6
024 7 _a10.1007/978-1-4614-5746-6
_2doi
050 4 _aQA8.9-10.3
072 7 _aPBC
_2bicssc
072 7 _aPBCD
_2bicssc
072 7 _aMAT018000
_2bisacsh
082 0 4 _a511.3
_223
100 1 _aSrivastava, Shashi Mohan.
_eauthor.
245 1 2 _aA Course on Mathematical Logic
_h[electronic resource] /
_cby Shashi Mohan Srivastava.
250 _a2nd ed. 2013.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXII, 198 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x0172-5939
505 0 _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.
520 _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
650 0 _aMathematics.
650 0 _aComputer science.
650 0 _aAlgebra.
650 0 _aLogic, Symbolic and mathematical.
650 1 4 _aMathematics.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aMathematical Logic and Formal Languages.
650 2 4 _aAlgebra.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461457459
830 0 _aUniversitext,
_x0172-5939
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-5746-6
912 _aZDB-2-SMA
999 _c95491
_d95491