Combinatorial set theory: with a gentle introduction to forcing
London; New York
Springer
c2012
xvi, 453 p.: ill.
Springer monographs in mathematics, 9341-2837
Includes bibliographical references and indexes
Lorenz J. Halbeisen
1.The setting -- 2. Overture: Ramsey's theorem -- 3. The axioms of Zermelo-Fraenkel set theory -- 4. Cardinal relations in ZF only -- 5. The axiom of choice -- 6. How to make two balls from one -- 7. Models of set theory with atoms -- 8. Twelve cardinals and their relations -- 9. The shattering number revisited -- 01. Happy families and their relatives -- 11. Coda: a dual form of Ramsey's theorem -- 21. The idea of forcing -- 31. Martin's axiom -- 41. The notion of forcing -- 51. Models of finite fragments of set theory -- 61. Proving unprovability -- 71. Models in which AC fails -- 81. Combining forcing notions -- 91. Models in which p=c -- 02. Properties of forcing extensions -- 12. Cohen forcing revisited -- 22. Silver-like forcing notions -- 32. Miller forcing -- 42. Mathias forcing -- 52. On the existence of Ramsey ultrafilters -- 62. Combinatorial properties of sets of partitions -- 72. Suite