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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 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.
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.
From the reviews:
"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)
"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)
"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)
From the reviews of the second edition:
"This very sophisticated work deals with what the author presents as proof of Gödel's completeness and incompleteness theorems in precise mathematical terms. ... This rigorous book is appropriate for graduate students or very talented undergraduates." (James Van Speybroeck, Computing Reviews, April, 2013)
"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)
"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)
"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)
From the reviews of the second edition:
"This very sophisticated work deals with what the author presents as proof of Gödel's completeness and incompleteness theorems in precise mathematical terms. ... This rigorous book is appropriate for graduate students or very talented undergraduates." (James Van Speybroeck, Computing Reviews, April, 2013)
Reviews from the first edition: "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)