Overview
- Offers a rigorous and inviting introduction to logic that inspires further study in logic
- Showcases connections to other areas of mathematics, including number theory, algebra, and combinatorics
- Versatile and appealing to graduate students in mathematics, computer science, and philosophy
Part of the book series: Graduate Texts in Mathematics (GTM, volume 301)
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Keywords
- Mathematical logic textbook
- Completeness theorem
- Incompleteness theorem
- Quantifier elimination
- Model theory introduction
- Computability introduction
- Hilbert's 10th problem
- graduate mathematical logic
- logic for philosophy
- logic for computer science
- Marker GTM
- quantifier elimination
- Godel's completeness
- ultraproducts
- Turing reducibility
- Godel's incompleteness
- Peano arithmetic
About this book
In addition to covering the essentials, the author’s intention in writing this text is to entice the reader to further study mathematical logic. There is no current “standard text” for a first graduate course in mathematical logic and this book will fill that gap. While there is more material than could be covered in a traditional one semester course, an instructor can cover the basics and still have the flexibility to choose several weeks’ worth of interesting advanced topics that have been introduced. The text can and will be used by people in various courses with different sorts of perspectives. This versatility is one of the many appealing aspects of this book. A list of suggested portions to be covered in a single course is provided as well as a useful chart which maps chapter dependencies. Additionally, a motivated student will have ample material for further reading.
New definitions, formalism, and syntax have been streamlined to engage thereader quickly into the heart of logic and to more sophisticated topics. Part I and Part IV center on foundational questions, while Part III establishes the fundamentals of computability. Part II develops model theory, highlighting the model theory of the fields of real and complex numbers. The interplay between logic and other areas of mathematics, notably algebra, number theory, and combinatorics, are illustrated in Chapters 5, 6, 8, 14, and 16. For most of the text, the only prerequisite is mathematical maturity. The material should be accessible to first year graduate students or advanced undergraduates in mathematics, graduate students in philosophy with a solid math background, or students in computer science who want a mathematical introduction to logic. Prior exposure to logic is helpful but not assumed.
Authors and Affiliations
About the author
David Marker is Professor Emeritus of Mathematics at the University of Illinois at Chicago where he was Liberal Arts & Sciences Distinguished Professor and a Fellow of the American Mathematical Society. His research interests lie in model theory and its applications. His textbook, Model Theory: An Introduction, which appeared as GTM 217 in 2002, was awarded the Association of Symbolic Logic Shoenfield Prize for expository writing.
Bibliographic Information
Book Title: An Invitation to Mathematical Logic
Authors: David Marker
Series Title: Graduate Texts in Mathematics
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Hardcover ISBN: 978-3-031-55367-7Due: 30 June 2024
Softcover ISBN: 978-3-031-55370-7Due: 30 June 2024
eBook ISBN: 978-3-031-55368-4Due: 30 June 2024
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XVIII, 357
Number of Illustrations: 7 b/w illustrations