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Description of  Godel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics

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. i will be very grateful when you support me and buy Or Renew Your Premium from my Blog links i appreciate your support Too much as it will help me to post more and more Without You And Your Support We Can’t Continue Thanks For Buying Premium From My Links For Support