Gödel's Theorems and Zermelo's Axioms

A Firm Foundation of Mathematics

Lorenz Halbeisen, Regula Krapf

$178.95 $143.01

Hardback

Not in-store but you can order this
How long will it take?

Availability Information

We source books from suppliers in Australia and overseas. For books we don't currently have in stock, the time it takes to get them from our suppliers can vary widely - from a few days to a few months - so we check each book with each supplier to determine the expected time it will take to be supplied to us.

We then advise you accordingly. If the time taken to get any book is too long for you, you can let us know and we will cancel or adjust your order, and refund as required.

To find out the anticipated arrival time for specific items prior to ordering, please contact us by phone or email:

Phone +61 2 9264 3111, or 1800 4 BOOKS (1800 4 26657) if outside Sydney:
option 1 Abbey's Bookshop (Crime, History, Science, Kids & more) • info@abbeys.com.au
option 2 Language Book Centre (ESL & Foreign Languages) • language@abbeys.com.au
option 3 Galaxy Bookshop (Sci-fi, Fantasy, Romance, Graphic Novels) • sf@galaxybooks.com.au

QTY:

English

Birkhauser Verlag AG
11 May 2025

Mathematical foundations; Mathematical logic

This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel’s classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel’s second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on Zermelo’s axioms, containing also a presentation of Gödel’s constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers. In addition, the corrected, revised and extended second edition now provides detailed solutions to all exercises.

The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory.

By: Lorenz Halbeisen, Regula Krapf
Imprint: Birkhauser Verlag AG
Country of Publication: Switzerland
Edition: Second Edition 2025
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783031851056
ISBN 10: 3031851056
Pages: 342
Publication Date: 11 May 2025
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

0. A Framework for Metamathematics.- Part I Introduction to First-Order Logic.- 1 Syntax: The Grammar of Symbols.- 2 The Art of Proof.- 3 Semantics: Making Sense of the Symbols.- Part II Gödel’s Completeness Theorem.- 4 Maximally Consistent Extensions.- 5 The Completeness Theorem.- 6 Language Extensions by Definitions.- Part III Gödel’s Incompleteness Theorems.- 7 Countable Models of Peano Arithmetic.- 8 Arithmetic in Peano Arithmetic.- 9 Gödelisation of Peano Arithmetic.- 10 The First Incompleteness Theorem.- 11 The Second Incompleteness Theorem.- 12 Completeness of Presburger Arithmetic.- Part IV The Axiom System ZFC.- 13 The Axioms of Set Theory (ZFC).- 14 Models of Set Theory.- 15 Models and Ultraproducts.- 16 Models of Peano Arithmetic.- 17 Models of the Real Numbers.- Tautologies.- Solutions.- References.- Index.

Lorenz Halbeisen is Professor of Logic and Set Theory at the ETH Zürich. Regula Krapf is Senior Academic Councilor at the University of Bonn since 2023.