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A Course on Mathematical Logic
— Feb 15, 2008

/lp/springer-e-books/a-course-on-mathematical-logic-mWWhDNvuXi

- Publisher
- Springer New York
- Copyright
- Copyright © Springer Basel AG
- DOI
- 10.1007/978-0-387-76277-7
- Publisher site
- See Book on Publisher Site

This book is written on the occassion of the birth centenary year of Kurt G¨ odel (1906–1978), the most exciting logician of all times, whose disc- eries shook the foundations of mathematics. His beautiful technique to - amine the whole edi?ce of mathematics within mathematics itself has been likened, not only ?guratively but also in precise technical terms, to the - sicofBachanddrawingsofEscher(4).Ithadadeepimpactonphilosophers andlinguists.Inaway,itusheredintheeraofcomputers.Hisideaofari- metization of formal systems led to the discovery of a universal computer program that simulates all programs. Based on his incompleteness th- rems, physicists have propounded theories concerning arti?cal intelligence and the mind–body problem (10). ThemaingoalofthisbookistostateandproveG¨ odel’scompletenessand incompleteness theorems in precise mathematical terms. This has enabled us to present a short, distinctive, modern, and motivated introduction to mathematical logic for graduate and advanced undergraduate students of logic, set theory, recursion theory, and computer science. Any mathema- cian who is interested in knowing what mathematical logic is concerned with and who would like to learn the famous completeness and incomple- ness theorems of G¨ odel should also ?nd this book particularly convenient. Thetreatmentisthoroughlymathematical, andtheentiresubjecthasbeen approachedlike anyotherbranchofmathematics. Seriouse?ortshavebeen madetomakethebooksuitableforbothinstructionalandself-readingp- poses.Thebookdoesnotstrivetobeacomprehensiveencyclopediaoflogic, xPreface nor does it broaden its audience to linguists and philosophers. Still, it gives essentially all the basic concepts and results in mathematical logic.; This book provides a distinctive, well-motivated introduction to mathematical logic. It starts with the definition of first order languages, proceeds through propositional logic, completeness theorems, and finally the two Incompleteness Theorems of Godel. ; This book is written on the occassion of the birth centenary year of Kurt G¨ odel (1906–1978), the most exciting logician of all times, whose disc- eries shook the foundations of mathematics. His beautiful technique to - amine the whole edi?ce of mathematics within mathematics itself has been likened, not only ?guratively but also in precise technical terms, to the - sicofBachanddrawingsofEscher(4).Ithadadeepimpactonphilosophers andlinguists.Inaway,itusheredintheeraofcomputers.Hisideaofari- metization of formal systems led to the discovery of a universal computer program that simulates all programs. Based on his incompleteness th- rems, physicists have propounded theories concerning arti?cal intelligence and the mind–body problem (10). ThemaingoalofthisbookistostateandproveG¨ odel’scompletenessand incompleteness theorems in precise mathematical terms. This has enabled us to present a short, distinctive, modern, and motivated introduction to mathematical logic for graduate and advanced undergraduate students of logic, set theory, recursion theory, and computer science. Any mathema- cian who is interested in knowing what mathematical logic is concerned with and who would like to learn the famous completeness and incomple- ness theorems of G¨ odel should also ?nd this book particularly convenient. Thetreatmentisthoroughlymathematical, andtheentiresubjecthasbeen approachedlike anyotherbranchofmathematics. Seriouse?ortshavebeen madetomakethebooksuitableforbothinstructionalandself-readingp- poses.Thebookdoesnotstrivetobeacomprehensiveencyclopediaoflogic, xPreface nor does it broaden its audience to linguists and philosophers. Still, it gives essentially all the basic concepts and results in mathematical logic.; Syntax of First-Order Logic.- Semantics of First-Order Languages.- Propositional Logic.- Proof and Metatheorems in First-Order Logic.- Completeness Theorem and Model Theory.- Recursive Functions and Arithmetization of Theories.- Incompleteness Theorems and Recursion Theory.; From the reviews: "This is an introductory textbook on modern mathematical logic, aimed at upper-level undergraduates. … The book is well-equipped with examples … ." (Allen Stenger, MathDL, July, 2008) "In this work, which provides an introduction to mathematical logic, Srivastava … indicates that his main goal is to ‘state and prove Gödel’s completeness and incompleteness theorems in precise mathematical terms.’ … the author presents the material in a clear fashion, with consistent and understandable notation. The book includes a number of exercises for the student to attempt and examples from a variety of areas in mathematics for the student to review. … Summing Up: Recommended. Advanced upper-division undergraduates, graduate students, faculty." (S. L. Sullivan, Choice, Vol. 46 (4), December, 2008) "The main goal of this book is to give a motivated introduction to mathematical logic for graduated and advanced undergraduate students of logic, set theory, recursion theory and computer science. Its intended audience includes also all mathematicians who are interested in knowing what mathematical logic is dealing with. … 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, Vol. 1140, 2008) ; This is a short, distinctive, modern, and motivated introduction to mathematical logic for senior undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in knowing what logic is concerned with and who would like to learn Gödel’s incompleteness theorems should find this book particularly convenient. The treatment is thoroughly mathematical, and the entire subject has been approached like a branch of mathematics. Serious efforts have been made to make the book suitable for the classroom as well as for self-reading. The book does not strive to be a comprehensive encyclopedia of logic. Still, it gives essentially all the basic concepts and results in mathematical logic. The book 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. The main prerequisite for this book is the willingness to work at a reasonable level of mathematical rigor and generality. Shashi Mohan Srivastava is a Professor at the Indian Statistical Institute, Kolkata, India. He is also the author of A Course on Borel Sets, GTM 180. ; Written in a clear, concise style Contains numerous exercises and examples Employs Godels completeness and incompleteness theorems to motivate the entire text Modern language and notation will appeal to undergrads as well as graduate students ; US

**Published: ** Feb 15, 2008

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