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Gödel's Theorems and Zermelo's Axioms

By Lorenz Halbeisen

Gödel's Theorems and Zermelo's Axioms Mathematics

Gödel's Theorems and Zermelo's Axioms

0 - Default Title
Description
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.
Product details
Edition:
2
Number of Pages:
356
Release Date:
2025-05-11
Publication Date:
2025-05-11
Publisher:
Birkhäuser
Languages:
Original: English
ISBN10:
3031851056
ISBN13:
9783031851056
GPSR Manufacturer Reference:
[email protected]
Weight:
697 g
Height:
160 cm
Width:
241 cm
Thickness:
25 cm
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