Gödel's theorems and Zermelo's axioms : a firm foundation of mathematics

Gödel's theorems and Zermelo's axioms : a firm foundation of mathematics / Lorenz Halbeisen, Regula Krapf.

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...

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Bibliographic Details
Main Authors: Halbeisen, Lorenz (Author), Krapf, Regula (Author)
Format: eBook
Language:English
Published: Cham, Switzerland : Birkhäuser, [2020]
Subjects:
Gödel's theorem.
Set theory.
Logic, Symbolic and mathematical.
Lógica matemática
Set theory
Gödel's theorem
Logic, Symbolic and mathematical
Online Access:Click for online access
Table of Contents:
  • A Natural Approach to Natural Numbers
  • Part I Introduction to First-Order Logic
  • Syntax: The Grammar of Symbols
  • Semantics: Making Sense of the Symbols
  • Soundness & Completeness
  • Part II Gödel's Completeness Theorem
  • Maximally Consistent Extensions
  • Models of Countable Theories
  • The Completeness Theorem
  • Language Extensions by Definitions
  • Part III Gödel's Incompleteness Theorems
  • Models of Peano Arithmetic and Consequences for Logic
  • Arithmetic in Peano Arithmetic
  • Gödelisation of Peano Arithmetic
  • The Incompleteness Theorems
  • The Incompleteness Theorems Revisited
  • Completeness of Presburger Arithmetic
  • Models of Arithmetic Revisited
  • Part IV Zermelo's Axioms
  • Axioms of Set Theory
  • Models of Set Theory
  • Models of the Natural and the Real Numbers
  • Tautologies.

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