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Springer Undergraduate Mathematics Series

Sets, Models and Proofs

Authors: Moerdijk, Ieke, van Oosten, Jaap

  • 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
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eBook $29.99
price for USA in USD (gross)
  • ISBN 978-3-319-92414-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
price for USA in USD
  • ISBN 978-3-319-92413-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

Both authors have extensive experience in teaching the material covered in this book, and have been active researchers in mathematical logic and related fields. Ieke Moerdijk co-authored the influential Springer text  "Sheaves in Geometry and Logic, a First Course in Topos Theory", together with Saunders Mac Lane. Jaap van Oosten is an expert on realizability models for systems of constructive logic, and is the author of a comprehensive monograph on the subject: "Realizability: An Introduction to its Categorical Side" . 

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Table of contents (4 chapters)

Buy this book

eBook $29.99
price for USA in USD (gross)
  • ISBN 978-3-319-92414-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
price for USA in USD
  • ISBN 978-3-319-92413-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Sets, Models and Proofs
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-92414-4
DOI
10.1007/978-3-319-92414-4
Softcover ISBN
978-3-319-92413-7
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XIV, 141
Number of Illustrations
39 b/w illustrations
Topics