Combinatorial Set Theory

Part I. Preliminary

1. The Setting
Lorenz J. Halbeisen

2. First-Order Logic in a Nutshell
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3. Axioms of Set Theory
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Part II. Topics in Combinatorial Set Theory

4. Overture: Ramsey’s Theorem
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5. Cardinal Relations in ZF Only
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6. Forms of Choice
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7. How to Make Two Balls from One
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8. Models of Set Theory with Atoms
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9. Thirteen Cardinals and Their Relations
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10. The Shattering Number Revisited
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11. Happy Families and Their Relatives
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12. Coda: A Dual Form of Ramsey’s Theorem
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Part III. Part III

13. The Idea of Forcing
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14. Martin’s Axiom
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15. The Notion of Forcing
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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

Keywords: Mathematics, Mathematical Logic and Foundations, Combinatorics