Combinatorial Set Theory

1. The Setting
Lorenz J. Halbeisen

2. Overture: Ramsey’s Theorem
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3. The Axioms of Zermelo–Fraenkel Set Theory
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4. Cardinal Relations in ZF Only
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5. The Axiom of Choice
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6. How to Make Two Balls from One
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7. Models of Set Theory with Atoms
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8. Twelve Cardinals and Their Relations
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9. The Shattering Number Revisited
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10. Happy Families and Their Relatives
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11. Coda: A Dual Form of Ramsey’s Theorem
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12. The Idea of Forcing
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13. Martin’s Axiom
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14. The Notion of Forcing
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15. Models of Finite Fragments of Set Theory
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16. Proving Unprovability
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17. Models in Which AC Fails
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18. Combining Forcing Notions
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19. Models in Which p = c

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20. Properties of Forcing Extensions
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21. Cohen Forcing Revisited
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22. Silver-Like Forcing Notions
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23. Miller Forcing
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24. Mathias Forcing
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25. On the Existence of Ramsey Ultrafilters
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26. Combinatorial Properties of Sets of Partitions
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27. Suite
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Keywords: Mathematics, Mathematical Logic and Foundations