Gödel's Theorems and Zermelo's Axioms A Firm Foundation of Mathematics /
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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| Główni autorzy: | , |
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| Format: | Elektroniczne E-book |
| Język: | angielski |
| Wydane: |
Cham :
Springer Nature Switzerland : Imprint: Birkhäuser,
2025.
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| Wydanie: | 2nd ed. 2025. |
| Hasła przedmiotowe: | |
| Dostęp online: | https://doi.org/10.1007/978-3-031-85106-3 |
| Etykiety: |
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Spis treści:
- 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.