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Birkhauser Gödel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics

Name: Godel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics
Brand: Birkhauser
Price: 41.78 GBP
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Mathematical Logic

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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 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.

Product Specifications

Brand: Birkhauser
Format: paperback
ASIN: 3030522814
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Foundations > Mathematical Logic
Domain: Amazon UK
Release Date: 17 October 2021
Listed Since: 20 September 2021

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Birkhauser Gödel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics

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