G del s Theorems and Zermelo s Axioms is popular PDF and ePub book, written by Lorenz Halbeisen in 2020-10-16, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, G del s Theorems and Zermelo s Axioms can be Read Online from any device for your convenience.
G del s Theorems and Zermelo s Axioms Book PDF Summary
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.
Detail Book of G del s Theorems and Zermelo s Axioms PDF
- Author : Lorenz Halbeisen
- Release : 16 October 2020
- Publisher : Springer Nature
- ISBN : 9783030522797
- Genre : Mathematics
- Total Page : 236 pages
- Language : English
- PDF File Size : 14,6 Mb
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