Overview
- New edition includes countable categoricity, analyzed using examples from the first two parts of the book
- Presents an introduction to formal mathematical logic and set theory
- Presents simple yet nontrivial results in modern model theory
Part of the book series: Springer Graduate Texts in Philosophy (SGTP, volume 4)
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Table of contents (20 chapters)
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Front Matter
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Logic, Sets, and Numbers
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Front Matter
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Relations, Structures, Geometry
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Front Matter
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Inference, Models, Categoricity and Diversity
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Front Matter
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Keywords
- first-order logic introduction
- Abstract symmetries
- Number system development
- Model theory
- Formal arithmetic
- Tameness mathematical structures
- Axiomatic set theory
- Compactness Theorem
- Logical visibility
- first-order logic applications
- complexity mathematical structures
- Applied compactness theorem
- geometry definable sets
- mathematical structure relations
- logical visibility
- language of modern mathematics
- recent developents model theory
- Ramsey theory
About this book
This textbook is a second edition of the successful, Mathematical Logic: On Numbers, Sets, Structures, and Symmetry. It retains the original two parts found in the first edition, while presenting new material in the form of an added third part to the textbook. The textbook offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions.
Part I, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are usedto study and classify mathematical structures. The added Part III to the book is closer to what one finds in standard introductory mathematical textbooks. Definitions, theorems, and proofs that are introduced are still preceded by remarks that motivate the material, but the exposition is more formal, and includes more advanced topics. The focus is on the notion of countable categoricity, which analyzed in detail using examples from the first two parts of the book. This textbook is suitable for graduate students in mathematical logic and set theory and will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Mathematical Logic
Book Subtitle: On Numbers, Sets, Structures, and Symmetry
Authors: Roman Kossak
Series Title: Springer Graduate Texts in Philosophy
DOI: https://doi.org/10.1007/978-3-031-56215-0
Publisher: Springer Cham
eBook Packages: Religion and Philosophy, Philosophy and Religion (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Hardcover ISBN: 978-3-031-56214-3Published: 19 April 2024
eBook ISBN: 978-3-031-56215-0Published: 18 April 2024
Series ISSN: 2627-6046
Series E-ISSN: 2627-6054
Edition Number: 2
Number of Pages: XVI, 257
Number of Illustrations: 29 b/w illustrations
Topics: Philosophy of Mathematics, Mathematical Logic and Foundations, Arithmetic and Logic Structures, Logic, Applications of Mathematics