Gödel's Theorems and Zermelo's Axioms

A Firm Foundation of Mathematics

AvLorenz Halbeisen,Regula Krapf

Inbunden, Engelska, 2025

694 kr

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Häftad

631 kr

Beskrivning

This book provides a concise and self-contained introduction to the foundations of mathematics. 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.

Produktinformation

Utgivningsdatum:2025-05-11
Mått:155 x 235 x 26 mm
Vikt:698 g
Format:Inbunden
Språk:Engelska
Antal sidor:342
Upplaga:2
Förlag:Birkhauser Verlag AG
ISBN:9783031851056

Utforska kategorier

Matematikens grunder inom Naturvetenskap och teknik

Mer om författaren

Lorenz Halbeisen is Professor of Logic and Set Theory at the ETH Zürich.Regula Krapf is Senior Academic Councilor at the University of Bonn since 2023.

Innehållsförteckning

0. A Framework for Metamathematics.- Part I Introduction to First-Order Logic.- 1 Syntax: The Grammar of Symbols.- 2 The Art of Proof.- 3 Semantics: Making Sense of the Symbols.- Part II Gödel’s Completeness Theorem.- 4 Maximally Consistent Extensions.- 5 The Completeness Theorem.- 6 Language Extensions by Definitions.- Part III Gödel’s Incompleteness Theorems.- 7 Countable Models of Peano Arithmetic.- 8 Arithmetic in Peano Arithmetic.- 9 Gödelisation of Peano Arithmetic.- 10 The First Incompleteness Theorem.- 11 The Second Incompleteness Theorem.- 12 Completeness of Presburger Arithmetic.- Part IV The Axiom System ZFC.- 13 The Axioms of Set Theory (ZFC).- 14 Models of Set Theory.- 15 Models and Ultraproducts.- 16 Models of Peano Arithmetic.- 17 Models of the Real Numbers.- Tautologies.- Solutions.- References.- Index.