Set Theory

Table of Contents

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