Combinatorial Set Theory

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.

• Erscheinungsdatum: 26.05.2025
• Autor/Autorin: Lorenz J. Halbeisen
• Reihe: Mathematics and Statistics (R0)
• Format: E-Book
• Dateiformat: PDF
• Kopierschutz: Wasserzeichen
• Dateigröße: 10.2 MB
• Auflage: Third Edition 2025
• Verlag: SPRINGER
• Sprache: Englisch
• Umfang: 616 Seiten
• ISBN: 9783031917523
• Lieferung: Sofort per Download
• Hinweis: Sofort per Download lieferbar. Kein physischer Versand.
• Kompatibilität: Lesbar auf Geräten und Apps mit PDF-Unterstützung.