Goedel's Theorems and Zermelo's Axioms
portes grátis
Goedel's Theorems and Zermelo's Axioms
A Firm Foundation of Mathematics
Halbeisen, Lorenz; Krapf, Regula
Birkhauser Verlag AG
04/2025
342
Dura
Inglês
9783031851056
Pré-lançamento - envio 15 a 20 dias após a sua edição
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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 Goedel's Completeness Theorem.- 4 Maximally Consistent Extensions.- 5 The Completeness Theorem.- 6 Language Extensions by Definitions.- Part III Goedel's Incompleteness Theorems.- 7 Countable Models of Peano Arithmetic.- 8 Arithmetic in Peano Arithmetic.- 9 Goedelisation 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.
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mathematical logic;set theory;completeness theorem;incompleteness theorem;non-standard models;Peano arithmetic;Presburger arithmetic;constructible universe
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 Goedel's Completeness Theorem.- 4 Maximally Consistent Extensions.- 5 The Completeness Theorem.- 6 Language Extensions by Definitions.- Part III Goedel's Incompleteness Theorems.- 7 Countable Models of Peano Arithmetic.- 8 Arithmetic in Peano Arithmetic.- 9 Goedelisation 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.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
