Combinatorial Set Theory With a Gentle Introduction to Forcing /
This book, now in a revised and extended third edition, provides a comprehensive and accessible introduction to modern axiomatic set theory. After an overview of basic notions in combinatorics and first-order logic, and discussing in great detail the axioms of set theory, the author outlines in the...
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| Format: | Electrònic eBook |
| Idioma: | anglès |
| Publicat: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
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| Edició: | 3rd ed. 2025. |
| Col·lecció: | Springer Monographs in Mathematics,
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| Accés en línia: | https://doi.org/10.1007/978-3-031-91752-3 |
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Taula de continguts:
- Part I: Preliminary
- 1 The Setting
- 2 First-Order Logic in a Nutshell
- 3 Axioms of Set Theory
- Part II: Topics in Combinatorial Set Theory
- 4 Overture: Ramsey's Theorem
- 5 Cardinal Relations in ZF Only
- 6 Forms of Choice
- 7 How to Make Two Balls from One
- 8 Models of Set Theory with Atoms
- 9 Thirteen Cardinals and Their Relations
- 10 The Shattering Number Revisited
- 11 Happy Families and Their Relatives
- 12 Coda: A Dual Form of Ramsey’s Theorem
- Part III: From Martin’s Axiom to Cohen’s Forcing
- 13 The Idea of Forcing
- 14 Martin's Axiom
- 15 The Notion of Forcing
- 16 Proving Unprovability
- 17 Models in Which AC Fails
- 18 Combining Forcing Notions
- 19 Models in Which p=c
- 20 Suslin’s Problem
- Part IV: Combinatorics of Forcing Extensions
- 21 Properties of Forcing Extensions
- 22 Cohen Forcing Revisited
- 23 Sacks Forcing
- 24 Silver-Like Forcing Notions
- 25 Miller Forcing
- 26 Mathias Forcing
- 27 Laver Forcing
- 28 How Many Ramsey Ultrafilters Exist?
- 29 Suite.