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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.
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.
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
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Grundlagen |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
xiv
141 S. 39 s/w Illustr. 141 p. 39 illus. |
| ISBN-13: | 9783319924137 |
| ISBN-10: | 3319924133 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-92413-7 |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Oosten, Jaap van
Moerdijk, Ieke |
| Auflage: | 1st edition 2018 |
| Hersteller: |
Springer Nature Switzerland
Springer International Publishing Springer International Publishing AG |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 9 mm |
| Von/Mit: | Jaap van Oosten (u. a.) |
| Erscheinungsdatum: | 06.12.2018 |
| Gewicht: | 0,248 kg |
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