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...
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| Autore principale: | |
|---|---|
| Natura: | Livre numérique |
| Lingua: | Anglais |
| Pubblicazione: |
London :
Springer London
[20..].
Cham : Springer Nature |
| Edizione: | 1st ed. 2012. |
| Serie: | Springer Monographs in Mathematics
|
| Soggetti: | |
| Accesso online: | 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 |
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| 100 | 1 | |a Halbeisen, Lorenz J., |d 19..- | |
| 245 | 1 | 0 | |a Combinatorial set theory : |b with a gentle introduction to forcing |c by Lorenz J. Halbeisen. |
| 250 | |a 1st ed. 2012. | ||
| 260 | |a London : |b Springer London. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Springer Monographs in Mathematics |x 2196-9922 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field | ||
| 650 | |a Forcing (mathématiques) | ||
| 650 | |a Théorie combinatoire des ensembles | ||
| 776 | 0 | |0 157924815 |t Combinatorial set theory |o with a gentle introduction to forcing |f Lorenz J. Halbeisen |c London |n Springer |d 2012 |p 1 vol. (XVI-453 p.) |s Springer monographs in mathematics |z 978-1-447-12172-5 | |
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