Combinatorial set theory : with a gentle introduction to forcing
This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophi...
Gardado en:
| Autor Principal: | |
|---|---|
| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
London :
Springer London
[20..].
Cham : Springer Nature |
| Edición: | 1st ed. 2012. |
| Series: | Springer Monographs in Mathematics
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| Sujets: | |
| Acceso en liña: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Combinatorial set theory, with a gentle introduction to forcing, Lorenz J. Halbeisen, London, Springer, 2012, 1 vol. (XVI-453 p.), Springer monographs in mathematics, 978-1-447-12172-5 |
Table des matières:
- The Setting Overture: Ramsey's Theorem The Axioms of Zermelo-Fraenkel Set Theory Cardinal Relations in ZF only The Axiom of Choice How to Make Two Balls from One Models of Set Theory with Atoms Twelve Cardinals and their Relations The Shattering Number Revisited Happy Families and their Relatives Coda: A Dual Form of Ramsey's Theorem The Idea of Forcing Martin's Axiom The Notion of Forcing Models of Finite Fragments of Set Theory Proving Unprovability Models in which AC Fails Combining Forcing Notions Models in which p = c Properties of Forcing Extensions Cohen Forcing Revisited Silver-Like Forcing Notions Miller Forcing Mathias Forcing On the Existence of Ramsey Ultrafilters Combinatorial Properties of Sets of Partitions Suite