Gödel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics okumak kayıt olmadan

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

Ders Kitapları

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.

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29 Ekim 2011 28 Şubat 2018 18,9 x 0,2 x 24,6 cm Kolektif ERWIN N GRISWOLD Additional Contributors ROBERT H BORK 15 x 0,5 x 22 cm WADE H MCCREE Mdpi AG 18,9 x 0,6 x 24,6 cm 18,9 x 0,3 x 24,6 cm 30 Ekim 2011 28 Ekim 2011 3 Ocak 2017 1 Ocak 2017 18,9 x 0,4 x 24,6 cm 18,9 x 0,5 x 24,6 cm

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