Godel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics free ebook download.

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Godel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics free ebook download

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Mathematics

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Catalogue

Author(s):	Lorenz Halbeisen

Date:	2020	Format:	pdf	Language:	English	ISBN/ASIN:	3030522784
Pages:	234	OCR:		Quality:		ISBN13:
Uploader:	eternal	Upload Date:	7/28/2024 9:02:09 AM

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3030522784 pdf
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 Godel’s classical completeness and incompleteness theorems.
In particular, the book includes a full proof of Godel’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 Godel’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.
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	Title	Link	Password	Size (MB)	Thank to	Inform Admin
3267435	Book	https://nitroflare.com/view/15F5A68F3ABD...		3.00	eternal

Tags: Axioms Firm Foundation Godel Mathematics Theorems Zermelo

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