Overview
- Provides a concise introduction to mathematical logic for mathematics students
- Introduces models before formal proofs
- Includes a detailed presentation of naïve set theory as used in everyday mathematical reasoning
- Gives a detailed description of Gentzen-style proof trees and Gödel’s completeness theorem for first-order logic
- Contains over 100 exercises of varying difficulty
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas.
The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study.
The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.
Reviews
“This book is one of a few excellent textbooks for a one-semester introductory mathematical logic course for undergraduate students with relevant majors. It achieves a good balance between depth and brevity. It fits the needs of a student who wants to explore the subject but does not want to be bogged down by excessive demands of rigor before appreciation for mathematical logic can be developed. ... This book is short but self-contained and … interesting exercises complement the main theorems.” (Renling Jin, Mathematical Reviews, September, 2019)
Authors and Affiliations
About the authors
Bibliographic Information
Book Title: Sets, Models and Proofs
Authors: Ieke Moerdijk, Jaap van Oosten
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-319-92414-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-92413-7Published: 06 December 2018
eBook ISBN: 978-3-319-92414-4Published: 23 November 2018
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: XIV, 141
Number of Illustrations: 39 b/w illustrations
Topics: Structures and Proofs, Algebra