Combinatorial Set Theory With a Gentle Introduction to Forcing /

This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including R...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Halbeisen, Lorenz J. (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2017.
Έκδοση:2nd ed. 2017.
Σειρά:Springer Monographs in Mathematics,
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
Πίνακας περιεχομένων:
  • The Setting
  • First-Order Logic in a Nutshell
  • Axioms of Set Theory
  • Overture: Ramsey's Theorem
  • Cardinal Relations in ZF Only
  • Forms of Choice
  • How to Make Two Balls from One
  • Models of Set Theory with Atoms
  • Thirteen 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
  • Proving Unprovability
  • Models in Which AC Fails
  • Combining Forcing Notions
  • Models in Which p=c
  • Suslin’s Problem
  • Properties of Forcing Extensions
  • Cohen Forcing Revisited
  • Sacks Forcing
  • Silver-Like Forcing Notions
  • Miller Forcing
  • Mathias Forcing
  • How Many Ramsey Ultrafilters Exist?
  • Combinatorial Properties of Sets of Partitions
  • Suite.