Goedel's Theorems and Zermelo's Axioms - A Firm Foundation of Mathematics (Paperback, 1st ed. 2020)

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 Goedel's classical completeness and incompleteness theorems. In particular, the book includes a full proof of Goedel'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 the Zermelo's axioms, containing a presentation of Goedel'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. The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Release date:	October 2021
First published:	2020
Authors:	Lorenz Halbeisen • Regula Krapf
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	236
Edition:	1st ed. 2020
ISBN-13:	978-3-03-052281-0
Categories:	Books > Science & Mathematics > Mathematics > Mathematical foundations > General Promotions
LSN:	3-03-052281-4
Barcode:	9783030522810

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