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| Preface | |
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| Basics of set theory | |
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| Axiomatic set theory | |
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| Why axiomatic set theory? | |
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| The language and the basic axioms | |
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| Relations, functions, and Cartesian product | |
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| Relations and the axiom of choice | |
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| Functions and the replacement scheme axiom | |
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| Generalized union, intersection, and Cartesian product | |
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| Partial- and linear-order relations | |
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| Natural numbers, integers, and real numbers | |
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| Natural numbers | |
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| Integers and rational numbers | |
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| Real numbers | |
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| Fundamental tools of set theory | |
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| Well orderings and transfinite induction | |
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| Well-ordered sets and the axiom of foundation | |
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| Ordinal numbers | |
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| Definitions by transfinite induction | |
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| Zorn's lemma in algebra, analysis, and topology | |
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| Cardinal numbers | |
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| Cardinal numbers and the continuum hypothesis | |
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| Cardinal arithmetic | |
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| Cofinality | |
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| The power of recursive definitions | |
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| Subsets of R[superscript n] | |
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| Strange subsets of R[superscript n] and the diagonalization argument | |
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| Closed sets and Borel sets | |
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| Lebesgue-measurable sets and sets with the Baire property | |
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| Strange real functions | |
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| Measurable and nonmeasurable functions | |
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| Darboux functions | |
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| Additive functions and Hamel bases | |
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| Symmetrically discontinuous functions | |
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| When induction is too short | |
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| Martin's axiom | |
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| Rasiowa-Sikorski lemma | |
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| Martin's axiom | |
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| Suslin hypothesis and diamond principle | |
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| Forcing | |
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| Elements of logic and other forcing preliminaries | |
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| Forcing method and a model for [not sign]CH | |
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| Model for CH and [diamonds suit symbol] | |
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| Product lemma and Cohen model | |
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| Model for MA+[not sign]CH | |
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| Axioms of set theory | |
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| Comments on the forcing method | |
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| Notation | |
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| References | |
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| Index | |