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Index
Cover
Frontmatter
1. Preliminaries: Sets, Relations, and Functions
1. Dedekind: Numbers
Part Frontmatter
2. The Dedekind–Peano Axioms
3. Dedekind’s Theory of the Continuum
4. Postscript I: What Exactly Are the Natural Numbers?
2. Cantor: Cardinals, Order, and Ordinals
Part Frontmatter
5. Cardinals: Finite, Countable, and Uncountable
6. Cardinal Arithmetic and the Cantor Set
7. Orders and Order Types
8. Dense and Complete Orders
9. Well-Orders and Ordinals
10. Alephs, Cofinality, and the Axiom of Choice
11. Posets, Zorn’s Lemma, Ranks, and Trees
12. Postscript II: Infinitary Combinatorics
3. Real Point Sets
Part Frontmatter
13. Interval Trees and Generalized Cantor Sets
14. Real Sets and Functions
15. The Heine–Borel and Baire Category Theorems
16. Cantor–Bendixson Analysis of Countable Closed Sets
17. Brouwer’s Theorem and Sierpinski’s Theorem
18. Borel and Analytic Sets
19. Postscript III: Measurability and Projective Sets
4. Paradoxes and Axioms
Part Frontmatter
20. Paradoxes and Resolutions
21. Zermelo–Fraenkel System and von Neumann Ordinals
22. Postscript IV: Landmarks of Modern Set Theory
Backmatter
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