Gödel's Theorems and Zermelo's Axioms

Gödel's Theorems and Zermelo's Axioms
Author: Lorenz Halbeisen
Publisher: Springer Nature
Total Pages: 236
Release: 2020-10-16
Genre: Mathematics
ISBN: 3030522792

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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 the Zermelo’s axioms, containing 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. 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.


Gödel's Theorems and Zermelo's Axioms
Language: en
Pages: 236
Authors: Lorenz Halbeisen
Categories: Mathematics
Type: BOOK - Published: 2020-10-16 - Publisher: Springer Nature

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This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical lo
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Pages: 425
Authors: G.H. Moore
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

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This book grew out of my interest in what is common to three disciplines: mathematics, philosophy, and history. The origins of Zermelo's Axiom of Choice, as wel
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Language: en
Pages: 376
Authors: Peter Smith
Categories: Mathematics
Type: BOOK - Published: 2007-07-26 - Publisher: Cambridge University Press

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Peter Smith examines Gödel's Theorems, how they were established and why they matter.
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Language: en
Pages: 272
Authors: Stuart Shanker
Categories: Gödel's theorem
Type: BOOK - Published: 1989 - Publisher: Psychology Press

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A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significanc
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Language: en
Pages: 286
Authors: Raymond M. Smullyan
Categories: Mathematics
Type: BOOK - Published: 2012-07-04 - Publisher: Knopf

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Forever Undecided is the most challenging yet of Raymond Smullyan’s puzzle collections. It is, at the same time, an introduction—ingenious, instructive, ent