Description
Combinatorial Set Theory (2nd Ed., 2nd ed. 2017)
With a Gentle Introduction to Forcing
Springer Monographs in Mathematics Series
Author: Halbeisen Lorenz J.
Language: EnglishSubject for Combinatorial Set Theory:
Keywords
axiom of choice; Banach-Tarski paradox; cardinal characteristics; combinatorics of forcing; forcing constructions; forcing technique; infinite combinatorics; Martin's axiom; permutation models; Ramsey theory; Ramsey ultrafilters; set theory; Suslin's problem; MSC (2010): 03E35; 03E17; 03E25; 05D10; 03E30; 03E50; 03E05; combinatorics
Publication date: 06-2019
594 p. · 15.5x23.5 cm · Paperback
158.24 €
In Print (Delivery period: 15 days).
Add to cart the print on demand of Halbeisen Lorenz J.Publication date: 01-2018
Support: Print on demand
Description
/li>Contents
/li>Comment
/li>
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.
Provides a comprehensive introduction to the sophisticated technique of forcing
Includes Shelah’s astonishing construction of a model in which exactly 27 Ramsey ultrafilters exist
Offers topics and open problems for further study
Includes supplementary material: sn.pub/extras