Jaap van Oosten: Sets, Models and Proofs

Cover: 9783319924137 | Sets, Models and Proofs | Jaap van Oosten (u. a.) | Taschenbuch | xiv

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Beschreibung

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.

Über den Autor

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" .

Zusammenfassung

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

Inhaltsverzeichnis

Introduction.- 1 Sets.- 2 Models.- 3 Proofs.- 4 Sets Again.- Appendix: Topics for Further Study.- Photo Credits.- Bibliography.- Index.

Details

Erscheinungsjahr:	2018
Fachbereich:	Grundlagen
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Springer Undergraduate Mathematics Series
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
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Oosten, Jaap van Moerdijk, Ieke
Auflage:	1st ed. 2018
Hersteller:	Springer International Publishing Springer International Publishing AG Springer Undergraduate Mathematics Series
Maße:	235 x 155 x 9 mm
Von/Mit:	Jaap van Oosten (u. a.)
Erscheinungsdatum:	06.12.2018
Gewicht:	0,248 kg

Artikel-ID: 113608916