buchspektrum Internet-Buchhandlung

Neuerscheinungen 2018

Stand: 2020-02-01
Schnellsuche
ISBN/Stichwort/Autor
Herderstraße 10
10625 Berlin
Tel.: 030 315 714 16
Fax 030 315 714 14
info@buchspektrum.de

Ieke Moerdijk, Jaap van Oosten (Beteiligte)

Sets, Models and Proofs


1st ed. 2018. 2018. xiv, 141 S. 39 SW-Abb. 235 mm
Verlag/Jahr: SPRINGER, BERLIN; SPRINGER INTERNATIONAL PUBLISHING 2018
ISBN: 3-319-92413-3 (3319924133)
Neue ISBN: 978-3-319-92413-7 (9783319924137)

Preis und Lieferzeit: Bitte klicken


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